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In l:.xercises 1-8. a linear operator Ton n3 and a basis 8 for n3 are gien. Compwe

Elementary Linear Algebra: A Matrix Approach | 2nd Edition | ISBN: 9780131871410 | Authors: Lawrence E. Spence ISBN: 9780131871410 187

Solution for problem 5 Chapter 5.4

Elementary Linear Algebra: A Matrix Approach | 2nd Edition

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Elementary Linear Algebra: A Matrix Approach | 2nd Edition | ISBN: 9780131871410 | Authors: Lawrence E. Spence

Elementary Linear Algebra: A Matrix Approach | 2nd Edition

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Problem 5

In l:.xercises 1-8. a linear operator Ton n3 and a basis 8 for n3 are gien. Compwe [Till- and determine whether B is a basis for n3 con.ri.rting of eigenllec/OrS ofT.

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Consumer behavior 01/13/2016 ▯ Consumer behavior:  30,000 new products are introduced each year, 70-90% are withdrawn from the market within 12 months o Didn’t correctly identify with the target o Lack of communication and awareness ▯ ▯ Consumer behavior is the study of the process involved when individuals and groups select, purchase, use, or dispose of products, services, ideas, or experiences to satisfy needs and desires ▯  Influencer o Someone who can sway people when purchasing; can be known or not; can be online too (Ex: celebrity)  Community o Can be in person or online; typically those that share something in common (your people)  Consumer o Identifies a need or desire and then makes a purchase ▯ What kinds of decisions do we study  Acquisition o Buy, gift, borrow, steal, share, find, rent o Products or services o Acquirer is not always the user  Usage o Expected, unexpected, symbolic, ritual  Disposal o Recycling, trade-in, throw out, eBay ▯  Statistics focuses on numbers and outcomes  Economics assumes rational consumers  Psychology overlooks consumer context ▯ ▯ Consumer-brand relationships ▯  Self-concept attachment = user identity  Nostalgic attachment = link to past  Interdependence = part of daily routine  Love = emotional bonds ▯ ▯ ▯ ▯ ▯ Classifying consumer needs:  Need for affiliation  Need for power  Need for uniqueness ▯ ▯ Relationship marketing:  When a company makes an effort to interact with customers on a regular basis, giving customers the opportunity to maintain a bond with the company over time (Ex: amazon) ▯ ▯ Strategic marketing uses:  Making STP (Segmentation, target markets, positioning) decisions  Developing a customer oriented strategy (customer satisfaction)  Developing products and services o New, attributes, names, packaging  Making promotion and marketing communications decisions  Making pricing decisions  Making channel decisions ▯ ▯ Segmenting Consumers: Demographics: ▯ Demographics: Statistics that measure observable aspects of a population, such as:  Age  Gender  Family structure  Social class and income  Race and ethnicity  Geography ▯ ▯ Segmenting Consumers: Lifestyles: ▯ Psychographics  The way we feel about ourselves  The things we value  The things we do in our spare time ▯ ▯ Segmenting Consumers: External Influences  Social class  Reference groups  Family lifecycles  Group influences ▯ ▯ Role Theory: Everybody has a certain roles that they play (Ex: Wesley has a role as a football player) ▯ ▯ Deviant Consumer Behavior:  Addictive behavior: excessive behaviors brought on by chemical dependence  Compulsive behavior: irresistible urge to perform irrational act  Impulsive behavior: act on emotions ▯ ▯ ▯ ▯ ▯ Everything goes back to decisions, that’s why we start with it  Internal influences: What goes on inside (Ex: personality) that can influence decisions  External influences: The other things that go on (Ex: groups or social media) that can influence decisions  Marketing application: Not only how they relate, but how it can be used (Ex: Which ad campaign is more affective) ▯ ▯ Categories of decisions Cognitive o Rational thinking Habitual o Decisions that we make all the time (Ex: Always buy the same milk) Affective o Based on emotions, can be impulsive ▯ ▯ Cognitive: Used for really big decisions (Ex: College decision)  Need recognition o Current & Ideal o Experienced, remembered, and Expected  Information search o Pre-purchase & ongoing o Internal & external o What do we search for (Brand, attribute, evaluation, experiences) o Evaluation information **  Evaluation of alternatives o Inept, inert, and evoked o Categorization  Purchase decision  Post purchase behavior o Post-purchase dissonance o Post-purchase regret o Why we care ▯ ▯ Stage 1: Problem Recognition Occurs when consumer sees difference between current state and ideal state o What is the trigger o Need recognition: actual state declines o Opportunity recognition: ideal state moves upwards o Ex: Driving down the road and car breaks down, recognize that you need a car and that your car doesn’t work (Actual state) do I fix it or buy a new one (Ideal state) ▯ Can be positive or negative ▯ ▯ Do Marketers create problems We can create a new idea o Ideals are not constant o Rapid technology change o Do we all need the new iPhone We can create dissatisfaction with the actual o Marketers creating a problem and then solving it (Ex: iPhone) ▯ What are your goals Experienced utility: how something makes you feel in the moment Expected utility: how you expect something to make you feel Remembered utility: How you remember it and how that affects future options o They rarely align o What is the peak end rule  How someone felt at the peak and at the end is what matters ▯ ▯ Stage 2: Information search The Process by which we survey the environment for appropriate data to make a reasonable decision o Pre-Purchase or ongoing search  Pre-purchase: Ads and dealerships before buying a car  Ongoing: Online looking for houses but doesn’t need a house (Ex: Wonder what it would be like to live in Florida) o Internal or external search  Internal: Based on recall (Ex: If buying a car, go back and remember based on personal experience which car you liked and disliked)  External: Talking to people and looking at information (Ex: Word of mouth is most trusted) Marketers and/or third party sources/ ranking of some type (Ex: Advertising is least trusted)  Depends on MAO (motivation, ability, and opportunity)  Ability: experience (Ex: Do you have a washer and dryer, could you buy one today) ▯ ▯ What do we search for  Brands  Attributes o (Ex: Search by size, color, etc.)  Evaluations o (Ex: Search on products based on the number of stars)  Experiences o (Ex: Looking for vacation, so search for exotic or romantic vacation) ▯ ▯ ▯  ▯ ▯ What else affects search Importance of the task Involvement (more later) Perceived costs/benefits o If the costs of a making a decision is high, search a lot Expertise/knowledge o If any expert, may not have to search. If for the first time, will need to search Availability of information o May be times where you don’t have information, so search a little bit longer (Ex: Searching for a job next year but the job you want, you don’t have all the information to connect with them) Time o You don’t have all the time in the world to do your search (Ex: Cant go through 200 pages on the Google search) ▯ ▯ Do people search enough News Flash – people are lazy! Generally people “under search” o Look at only 1-2 sources before buying a car or major appliance o (Ex: It takes a while to buy a car so only go to a few dealerships) Search is not always accurate o Availability bias= recall information that is more accessible but not necessarily more diagnostic ▯ ▯ Evaluating information: (Schwartz Ch. 3) Availability o (Ex: Someone telling you it’s a bad car, that sticks with you) Salience and vividness o Salience: Pay attention to something if it is relevant o Vividness: The more we can make stories vivid, the better off we are (Read a story once, and never forget) Power of crowds o The reason reviews and ratings are so good, crowds do a better job predicting than a single person News o Where you get your news will affect how you evaluate information (Ex: If hard core conservative, watching Fox news only) Anchoring o When you have a piece of information and everything around that information is how you evaluate (Ex: Looking for running shoes but they are $75. Then you find a pair that is $40, if there is no difference, really like the $40 pair because anchored to the $75.) o Mostly used with pricing and sales Frames and accounts o Using words in a compelling way that either go your way or not go your way (Ex: If looking at presidential candidate and one person calls him a eradicate and the other calls him conservative, those words frame him.) ▯ ▯ Stage 3: Alternatives: Inept set: unacceptable options (Ex: Harvard or Texas State) Inert set: Options which consumers are indifference (Ex: Peter pan or Jif, if you don’t have a favorite brand it doesn’t matter) Evoked set/Consideration set: Subset of top of mind brands evaluated when making a choice (Ex: top three favorite choices, brands you are willing to consider) ▯ ▯ ▯ Why do we categorize Too much information Utter chaos without structure (Ex: Closet organization) Helps up learn We like to do it We are pretty good at it ▯ ▯ Categorization: Taxonomic o Similar objects in the same category (Ex: pants together) o Objects and categories have the same features  Lots of sharing within categories (Ex: shirts that are long sleeve and short sleeve)  Little sharing across categories (Ex: pants are not shirts) o 3 Types  Basic level (Fattening or non-fattening)  Superordinate level (Want to treat, have a dessert, have to make the decision first)  Subordinate level (The details) ▯ ▯ ▯ Ways to organize things ▯ ▯ More on categorization:  Graded structure o Some members represent the category better than others  Prototype o Best example of a category (Ex: If I say cell phone, IPhone first comes to mind) o Most easily recalled and becomes the standard for comparison  Goal derived o Contains things that are relevant to a goal (Ex: things to do on a Friday night) o We use rules & experiences to create these ▯ ▯ Strategic implications of product categorization:  First mover advantage o You become the prototype (Good place to be, Ex: IPhone)  Position a product o Position close/ away to prototype (Ex: Galaxy is similar to IPhone or Red bull positioning away from soft drink) o Position relevant to a goal (Ex: Orange juice is not just for breakfast anymore)  Consideration sets o Who gets in these  Identify competitors (Primary and secondary)  Create an exemplar product (proto-type)  Helps locate products in a store  Repositioning (Ex: Baking soda was positioned towards use, but then moved away so repositioned as a cleaner) ▯ ▯ ▯ Do this during “Big” purchases ▯ ▯ Stage 4: Purchase: ▯ ▯ Stage 5: Post-purchase:  Post purchase dissonance- a feeling of anxiety over whether the correct decision was made o Ask others o Look at reviews o Marketers do things like warranties, return policies, etc.  Post decision regret- a feeling that one should have purchased another option (Ex: Wanting to switch schools)  Why care after the sale o Repeat purchase o WOM (Word of mouth) o Low involvement purchases (most of the things we do) ▯ ▯ Theories:  Expectancy disconfirmation model (Ex: The expectation of new years eve) we have to manage this as marketers o Satisfaction and dissatisfaction o Actual performance compared to expectations  Attribution theory o Who gets credit or blame (If something gets wrong, who gets blamed)  Equity theory o We want fair exchanges where inputs = outputs (Ex: If we feel like were getting taken advantage of, then we punish them) o We punish firms that don’t act fairly ▯ ▯ ▯  Stimulus: everything we do in advertising (Ads)  First moment of truth: Shopper marketing o A lot of different things that go in the store (Coupons, what we use for promotion) o Understanding how people shop (Retail) o Experience: All of our customer management (Increasing loyalty and creating a relationship) o ZMOT: Digital (Social media and content marketing) ▯ ▯ Frameworks to understanding how customers make decisions:  Cognitive vs. emotional o Everything we have been doing so far is cognitive  High vs. low involvement o Everything we have been doing so far is high  Optimizing vs. satisfying  Compensatory vs. non-compensatory ▯ ▯ Cognitive vs. emotional decisions:  Cognitive (Driven by the mind) o Mind, weighted material  Emotional (Driven by the heart)  Or the combination of the two o (Ex: Colleges to choose from)  Factors to consider: (What we choose has influences) o Product type: The type of product that we are looking at has a lot of play  Utilitarian vs. Hedonic  Utilitarian: functional (Ex: Washer and dryer) Don’t have a lot of emotional investment  Hedonic: About the experience (Ex: Vacations or luxury materials) Emotion tied into it  Search vs. Experience  Search: (Ex: Never bought a washer and dryer, do some kind of search)  Experience o Context  How to use the product or who to use the product for. Situational involvement o Individual differences  Different people need different things (Need for cognition: need for information before making a decision) ▯ ▯ ▯ Conceptualizing involvement: ▯ ▯ * Don’t have to know all the details ▯ (Ex: Really love your phone, high involvement) ▯ ▯ Types of involvement:  Product o If it is a product that you really like (Ex: really into cars, higher involvement with cars) Even if you are an expert, still spend a lot of time because we like them.  Message o Really important when we think about the communication side (Advertising, PR) that are memorable (Ex: Super Bowl ads)  Situational o Certain things that are not a big deal, becomes a big deal (Ex: Have a couple bottles of wine, then if your boss is coming you spend a certain amount of time trying to pick out the best bottles) becomes a much bigger difference depending on the situation. ▯ ▯ Five Types of perceived risk: ▯ Risk drives involvement ▯ The more risk, the more you are going to search ▯ ▯  Monetary risk: (Ex: Buying a car)  Functional risk: (Ex: Bungee cord, want to make sure it works)  Physical risk (Ex: When you have kids, you have to buy a lot and do your homework. You don’t want to buy the crappy car seat)  Psychological risk (Ex: Sorority or Fraternity recruitment)  Social risk (Ex: Dress for prom) ▯ Most of the things we do are low involvement (Everyday stuff) ▯ ▯ How do we make decisions in low involvement:  Heuristics (These are shortcuts that make things easier) o Availability heuristics: What comes to mind (Ex: Lunch) o Base rate fallacy: The N=1 problem and personal experience (Ex: Jenny said its really great to go here, so I am going here) o Representative heuristics: Compare to the prototype o Marketers can use reviews and WOM to overcome these (Ex: Why social media is really important to us)  Satisficing  Focus on performance (“works best”), habits, brand loyalty and pricing (odds/even, deals) tactics o Odd/Even: If the price ends in an even number, we think high quality ▯ ▯ Habits:  Habitual decision making; little to no conscious effort o Priming: effect of environmental cues (Ex: Bakery, smells so good that we want it.) How the store is laid out is there for a reason o Co-variation: we assume certain attribute covary; for example, we believe that a clean car is in good mechanical condition (Ex: If I see something expensive, it must be good quality) o Country of origin: associate certain attributes with countries (Ex: Wine and France) or (Ex: If I am looking for Vodka, I want it to come from Russia) ▯ ▯ Bias:  Anchoring and adjusting= initial evaluation and adjust (Ex: Signals that this is a really great deal) It’s all about how we frame different options (Ex: If there are three options, we will usually choose the middle one) o Limit 6 per customer; showing the most expensive option  Confirmation bias= focus on existing beliefs and find information to support this (We do things to reinforce what we already believe)  Self positivity bias= bad things happen to others and not to me (Ex: Drinking and driving)  Negativity bias= weigh negative information more heavily (Ex: Two experiences outweigh 10 really good ratings) ▯ ▯ Optimizing vs. satisficing:  Which are you  Optimize/Maximize= only the best (Ex: Doing a lot of evaluating and information search)  Satisfice= good enough (Ex: Not really super worried about it, not necessarily going to put a lot of the effort in) Compensatory vs. Non-compensatory:  Compensatory= make trade off (nothing is perfect) o Cost/benefit analysis (Weighing good and bad, some good can make up for the bad) o TORA (Theory of reasoned action)  Non-compensatory= needs to meet a threshold o Lots of models (next slide)  What drives it o Size of the choice set. (A lot of choices) More makes it more difficult to choose o Importance of the attributes to the consumer o Resources available ▯ ▯ Non-compensatory models: (Look at note)  Conjunctive o Set minimum cutoffs o Start with all items and reject bad options o This product MUST meet my minimum requirements  Disjunctive o Set levels for attributes to reach o Start with no items and select good options o If this product does not have the features that I want, then it must have features that will make up for the loss  Lexicographic o Rank attributes by importance and compare one at a time o I will rank order attributes and narrow down alternatives by comparing the first rankings  Elimination by aspects o Set minimum level on most important attribute and then second, and then third and them forth o I will rank the attributes by importance and define the minimum required values ▯ ▯ Prospect theory  Losses loom larger than gains for consumers even if the outcomes are the same magnitude (Ex: If you loose 100, that weighs larger than gaining the same amount of money)  Endowment effect says that ownership increases the value (and loss) associated with an item (Ex: dealership letting you take a car home and try it out, becomes yours)  Marketers must find ways to reduce risk; carefully consider the amount of price increases and frame it as gains rather than losses ▯ Simple model of consumer behavior: ▯ ▯ ▯ ▯ Sensation and perception:  Sensation is the immediate response of our sensory receptors (eyes, ears, nose, mouth, fingers) (Ex: Abercrombie and perfume)  Perception is the process by which sensations are selected, organized, and interpreted o External stimuli trigger (Ex: In about an hour you are hungry for lunch, smell good smells from restaurants which triggers a need to go eat) o Senses input o Sensory marketing (Ex: All about colors/smells/etc., trying to understand how people react to different stimuli based on their senses) ▯ ▯ ▯ Team “Senses” Workshop:  Teams will be assigned a “sense” to research. The deliverable will be due Friday Feb 19 in class. Each team will make a quick 8 minute report on the sense – The purpose is to “teach” your colleagues about the role of your sense to marketing and consumer behavior. Be sure to have a good deck - you will be sharing it! ▯ ▯ ▯ Perception is reality:  Want to change reality Be an engineer (Everyone is going to have a different way of looking at things)  Want to change perception Be a marketer (We have to understand, is there ways to mold opinions and perceptions and what people think about our brands) o Perception can take a life of its own because of social media  Perception is crucial in consumer behavior because: o What customers perceive is what affects their actions o What is perceived in not necessarily what is “true” (Ex: Going to a restaurant and the food is okay, but your best friend loves the restaurant, imagine that the food and service has gotten better, well your perception is based on your previous experience. How do we affect this as marketers) ▯ ▯ ▯ Perception process:  Perception is constructive: people construct interpretations on the fly (We all have different perceptions of all brands and is a gut reaction)  The meanings are constructed as needed and are based on two major factors o The actual stimulus o Prior expectations (Ex: Had a BMW and know its bad while others would love one) There are certain colors that people perceive different perceptions (Ex: Blue is trustworthy) Key concepts in exposure: Exposure= the process which the consumer comes into contact with a stimulus. Gained through ads, POPs (point of purchase), shelf space, logos, product placement o Point of purchase: Standing in line and see gum on the side of the register o Shelf: There are reasons some items are at the top and some are in the middle o Logos: People don’t like changed logos, it messes with our perception o Product placement: Certain brands placed in movies We live in a world of messengers. Selective attention and selective retention o We decide what we pay attention to and what we decide to remember Sensory threshold= lowest intensity (Ex: Campbell’s has changed little things on their cans that aren’t noticeable but you would notice bigger changes) Key concepts in exposure: Absolute threshold= lowest point between “something” and “nothing” (Ex: Dog whistle, only dogs can hear) really cant tell consciously, just something that you feel Differential threshold= the ability of a sensory system to defect changes or differences between two stimuli (Everyone has a different differential threshold) Just noticeable difference (JND)= the minimum difference that can be detected between two stimuli; sometimes what this. Weber’s Law*= The stronger the initial stimulus, the greater the change must be to be noticed (Ex: Price must be 20% for reaction; cereal boxes must be vastly different to notice) o Times that we want to show a difference (Ex: Sale so it breaks through the clutter) o Times that we don’t want anyone to notice (Ex: Want to increase price, increase just enough but not enough so people notice) Marketing uses: Pricing (sales vs. increase); downsizing; brand names ▯ ▯ ▯ Attention: Attention is the extent to which processing activity is devoted to a particular stimulus o It is selective (Each person gets to select what they pay attention to, we cant pay attention to everything) As marketers we need to figure out a way to gain the information from customers o It is capable of being divided (You don’t just pay attention to one thing at a time, Ex: May be at home studying and watching TV and eating too) o It is limited (There is only so much you can do and only a certain amount of hours in the day) Consumers experiences sensory overload (Sometimes bombarded with stimuli) (Ex: Disney, lots of things going on and overwhelming) As Marketers we need to figure out how to break through that clutter Marketers need a break through the clutter ▯ ▯ Multitasking is not effective ▯ ▯ ▯ Factors leading to adaptation: ▯  Intensity: The less intense something is, the more likely you are to adapt to it Duration: If you experience it for a long time, you are more likely to adapt to it Discrimination: Things that are really simple usually blend into the background Exposure: If you are exposed to something a lot, that leads to adaptation (Ex: If you live next to a train, you eventually get used to it) Relevance: If it is irrelevant, you adapt to it, it is not really important to you How do marketers get attention:  Self relevant o Appeal to needs, values, and goals (Ex: Patagonia is big on being a Stuart of the environment) tap into value system. For need (Ex: See car ads but don’t really pay attention unless you need it) o Show source similar to audience (Ex: You would not have a Justin Beiber targeted to baby boomers) o Use drama (Find out a way to tell a story through drama)  Pleasant o Sex cells o Humor (Ex: Super bowl ads)  Surprising o Novelty  Ease of processing: If you can make a message as simple as possible, you can get their attention a lot better ▯ ▯ ▯ Interpretation:  Refers to the meaning we assign to sensory stimuli, which is based on a schema. Schema is a set of beliefs created off of experiences, what we’ve heard, and what we see ▯ ▯ ▯ Stimulus organization:  Gestalt: The whole is greater than the sum of the parts (Ex: Don’t look at celebrities and say they have a “good looking ear” we notice the beauty of the celebrity as a whole) o Closure: People perceive an incomplete picture as complete o Similarity: Consumers group together objects that share similar physical characteristics o Figure-ground: One part of the stimulus will dominate (the figure) while the other parts recede into the background (ground) ▯ Internal Influences for Consumer Behavior ▯ ▯ Memory: Is the process of acquiring information and storing it over time so that it will be available when needed External inputs-> Encoding (information is placed in memory)-> Storage (information is retained in memory)-> Retrieval (information stored in memory is found as needed) ▯ ▯ ▯ Memory System: Sensory memory: Temporary storage of sensory information o Capacity: High o Duration: Less than 1 second (vision) or a few seconds (hearing)  Short-term memory: Brief storage of information currently being used (Ex: Trying to remember a phone number) o Capacity: Limited o Duration: Less than 20 seconds  Long-term memory: Relatively permanent storage of information (Ex: Hearing a song, what you can pull out of your memory) o Capacity: Unlimited o Duration: Long or permanent ▯  Attention: (From sensory memory to short-term memory) Information that passes through an attention gate  Elaborative rehearsal: (From short-term memory to long-term memory) Information subjected to elaborative rehearsal or deep processing (Ex: Studying and sharing information for a test) ▯ ▯ \ ▯ ▯ ▯ More on types of memories:  Sensory memory: information is short lived (seconds) o Echoic: very brief memory for things we hear o Iconic: very brief memory for things we see  Short term memory (working): incoming information is encoded or interpreted in light of existing knowledge o Imagery: processing information in sensory form (See, hear, taste, feel, smell) o Discursive: processing information as words (Ex: Acronyms, we have a visual with the word NASA) o Chunking: Taking chunks of information and trying to remember it (Ex: Phone numbers or websites)  Long term memory: information stored for permanent use (If you have a strong connection context) o Autobiographical: knowledge about ourselves and our past o Semantic: general information about a category (Ex: When talking about cars, some people know general information while others know extensive information) ▯ ▯ ▯ Marketing implications – STM  Imagery processing can affect product liking and choice o (Ex: We buy some products for the imagery they provide like music or books)  Imagery can stimulate memories of past experiences o (Ex: Video games played as a kid, Pac Man)  Imagery can affect how much information we can process (Ex: Abercrombie, it looks the same everywhere and we can picture it)  Imagery may affect how satisfied we are with a product or consumption experience ▯ ▯ ▯ Marketing implications- LTM  Affects decision making o Really bad restaurant experiences  Promotes empathy and identifications o Characters or situations in ads makes you remember when that happened to you  Cues and preserve autobiographical memories o Nostalgia; digital cameras, scrapbooks, etc. ▯ ▯ ▯

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Chapter 5.4, Problem 5 is Solved
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Textbook: Elementary Linear Algebra: A Matrix Approach
Edition: 2
Author: Lawrence E. Spence
ISBN: 9780131871410

The answer to “In l:.xercises 1-8. a linear operator Ton n3 and a basis 8 for n3 are gien. Compwe [Till- and determine whether B is a basis for n3 con.ri.rting of eigenllec/OrS ofT.” is broken down into a number of easy to follow steps, and 31 words. Elementary Linear Algebra: A Matrix Approach was written by and is associated to the ISBN: 9780131871410. This textbook survival guide was created for the textbook: Elementary Linear Algebra: A Matrix Approach, edition: 2. This full solution covers the following key subjects: . This expansive textbook survival guide covers 34 chapters, and 2741 solutions. Since the solution to 5 from 5.4 chapter was answered, more than 260 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 5 from chapter: 5.4 was answered by , our top Math solution expert on 12/27/17, 07:57PM.

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In l:.xercises 1-8. a linear operator Ton n3 and a basis 8 for n3 are gien. Compwe