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Get Full Access to Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) - 3 Edition - Chapter 3 - Problem 3.7.13
Get Full Access to Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) - 3 Edition - Chapter 3 - Problem 3.7.13

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# Let j denote a row vector consisting entirely of 1s. Provethat a nonnegative matrix P is

ISBN: 9780538735452 298

## Solution for problem 3.7.13 Chapter 3

Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) | 3rd Edition

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Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) | 3rd Edition

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Problem 3.7.13

Let j denote a row vector consisting entirely of 1s. Provethat a nonnegative matrix P is a stochastic matrix ifand only if jP j.

Step-by-Step Solution:
Step 1 of 3

Monday, January 22, 2018 Stats Section 2.1 - Visualizing Variation in Numerical Data Distribution of a sample: organization of data, list that records the values that were observed and the frequencies of these values Frequency: the count of how many times the value occurred in the collection of data - The ﬁrst step to almost every statistical investigation is to visualize the distribution of the sample so that we can see patterns more easily - To examine distributions, we use a two-step process: • See it • Summarize it Two useful methods of for visualizing distributions are dot plot (simpler) and histograms (more common and useful) Dotplot: Put a dot above a number line where each value occurs to get a sense of frequency by seeing how high the dots stack up - Use when data set is small, and lack of tech Histograms Histogram: produce a smoother graphic by grouping observations into intervals, called bins, which are formed by dividing the number line into equal width and then counting how many observations fall into each bin - Rules need to be made: • For when an observation lands exactly on a boundary, just be consistent - Right/left-hand rule to put value on boundary into one bin • Using wider bins hides more details, but don’t make it too small, 3 is good Relative frequency Histograms - Variation on the histogram, change vertical axis from frequency to relative frequency • Relative frequency: a proportion, label is 0-1 - Ex- ﬁrst bin has 5 observations (out of 28), so 5/28=0.18 1

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##### ISBN: 9780538735452

The answer to “Let j denote a row vector consisting entirely of 1s. Provethat a nonnegative matrix P is a stochastic matrix ifand only if jP j.” is broken down into a number of easy to follow steps, and 24 words. The full step-by-step solution to problem: 3.7.13 from chapter: 3 was answered by , our top Math solution expert on 01/29/18, 04:03PM. This full solution covers the following key subjects: . This expansive textbook survival guide covers 7 chapters, and 1985 solutions. Since the solution to 3.7.13 from 3 chapter was answered, more than 295 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign), edition: 3. Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) was written by and is associated to the ISBN: 9780538735452.

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Let j denote a row vector consisting entirely of 1s. Provethat a nonnegative matrix P is