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# In Exercises 7–10, let H be the hyperplane | Ch 8.4 - 9E

ISBN: 9780321385178 62

## Solution for problem 9E Chapter 8.4

Linear Algebra and Its Applications | 4th Edition

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Linear Algebra and Its Applications | 4th Edition

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Problem 9E

In Exercises 7–10, let H be the hyperplane through the listed points.(a) Find a vector n that is normal to the hyperplane.(b) Find a linear functional f and a real number d such that H = [f : d].

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Week 12 notes th March 30 Notes Monte Carol Simulation  Use when decisions are made with random events  Decision Tree: only random events with discrete outcomes o Discrete outcome=countable or limited number of outcomes  Monte Carlo Simulation: random events w/ discrete and continuous outcomes o Continuous outcome=every possible outcome in a range o Can use parametric and structural sensitivity easily  =RAND(x) function o Generates random number between 0 and 0.99999… o Re-calculates by pressing F9 (on PC) o Every number is equally likely (uniform distribution) o If make a histogram of 1000 trials of RAND fxn, all bars should be equal height  Uniform distribution outside 0-1 o Ex. Get random number between 10 and 25:  10+(25-10) x RAND()  10= lower limit  (25-10)=range  Why at least 10 (lower limit) and rand can be anywhere between 0-1 so multiply by range to put outcome between 10-25 o Get random integer values between 60 and 75  RANDBETWEEN(60,75)  =RANDBETWEEN gives integer values only  Simulating 2 outcome discrete distributions o Ex. Simulate event that may happen with probability of 0.4  =IF(RAND()<0.4, 1, 0)  Why Rand will give number between 0-1 0-0.4 0.4-1 Hit flop 40% 60%  Binary 1=hit and 0=flop  Random Number from a Normal Distribution Normal Distribution 3 2 1 0 0 0.2 0.4 0.6 0.8 1 1.2   Ex. Mean=100, SD=20  NORM.INV(RAND, 100, 20)=will give number on x-axis  normal distribution probability  will create a norm distribution histogram  use rand fxn to replace probability Baby Lee’s Doughnuts Baby Lee’s Doughnuts stocks exactly 33 super-duper doughnuts every day. Each super-duper doughnut sells for $2. Unsold doughnuts are eaten by Baby Lee at the end of the day. Daily demand for super-duper doughnuts is a random event and is given by the following probability distribution. Develop a simulation model to determine the mean and standard deviation of daily revenue obtained from the sale of the super-duper doughnuts.  Decision tree 0.4 32 o 0.3 33 0.3 34  Make range from 0-1 with 3 possible outcomes3 sub-ranges  Boundary of ranges correspond with probabilities of each value 32 33 34 0 0.4 0.7 0.4 0.7 1 40% 30% 30%  In excel B C D E 2 Demand 32 33 34 3 Probability 0.4 0.3 0.3 Simulation Calculations  Demand: =IF(B10250")/1000 o Give percent chance that of donations being over$250  Percentage changes every time but stays in a certain range  Increase number of trialsnarrow range of answers

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##### ISBN: 9780321385178

The full step-by-step solution to problem: 9E from chapter: 8.4 was answered by , our top Math solution expert on 08/10/17, 10:08AM. This textbook survival guide was created for the textbook: Linear Algebra and Its Applications, edition: 4. The answer to “In Exercises 7–10, let H be the hyperplane through the listed points.(a) Find a vector n that is normal to the hyperplane.(b) Find a linear functional f and a real number d such that H = [f : d].” is broken down into a number of easy to follow steps, and 39 words. Linear Algebra and Its Applications was written by and is associated to the ISBN: 9780321385178. Since the solution to 9E from 8.4 chapter was answered, more than 280 students have viewed the full step-by-step answer. This full solution covers the following key subjects: Find, hyperplane, listed, exercises, let. This expansive textbook survival guide covers 65 chapters, and 1915 solutions.

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In Exercises 7–10, let H be the hyperplane | Ch 8.4 - 9E