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Show that if A is a square matrix that satisfies the equation A2 2A I O, then A1 2I A

Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) | 3rd Edition | ISBN: 9780538735452 | Authors: David Poole ISBN: 9780538735452 298

Solution for problem 3.3.45 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 | ISBN: 9780538735452 | Authors: David Poole

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

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Problem 3.3.45

Show that if A is a square matrix that satisfies the equation A2 2A I O, then A1 2I A. 46

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● Population Variance ○ If N is the number of values in a population with mean mu, and xi represents each individual in the population, the the population variance is found by: ○ σ 2 = sumN i=1 (xi − µ) 2 N ○ and the population standard deviation is the square root, σ = √ σ 2. ○ Most of the time we are working with a sample instead of a population. So the sample variance is found by: s 2 = Pn i=1 (xi − x¯) 2 n − 1 and the sample standard deviation is the square root, s = √ s 2. Where n is the number of observations (samples), xi is the value for the i th observation and x¯ is the sample mean. ○ By hand ­ find mean, square each scores, 1/(#­1)*(all sum square­ #*mean), then square root the ans = sd ○ If we change the data set by adding/subtract then the mean changes and sd and var remains the same ○ If multiplied or divided everything changes ● X means + sd ○ y=a+bx a and b are constants ○ mean(y)= a+b(mean(x)) ○ sd(y) = b(sd(x)) ○ var(y)=b^2(var(x)) ■ X mean (x) = 3 sd (x) = 0.5 ■ y= 3+2x mean(y) = 3+2(3) = 9 ○ sd(x) = 2(0.5) = 1 ● The function for the sample standard deviation in R is sd(data name$variable name) ● . ● Coefficient of Var

Step 2 of 3

Chapter 3, Problem 3.3.45 is Solved
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Textbook: Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign)
Edition: 3
Author: David Poole
ISBN: 9780538735452

The full step-by-step solution to problem: 3.3.45 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. The answer to “Show that if A is a square matrix that satisfies the equation A2 2A I O, then A1 2I A. 46” is broken down into a number of easy to follow steps, and 21 words. Since the solution to 3.3.45 from 3 chapter was answered, more than 316 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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Show that if A is a square matrix that satisfies the equation A2 2A I O, then A1 2I A