Can you help with question 1.6.1.c? 1.4.2 Solve the following systems and determine the number of degrees, of freedom:0 = Ex+ 7x – IT0 = Ex – Tx7 + Ix(a)X1 + 3x2 + 2x3 +4x4 02x1+x2+3x3 = 01.4.5 Let a1,.. ., a, be n linearly independent vectors in R". Prove that if a vector b in R" isorthogonal to all the vectors a1, ., an, then b = 0.1.5.1(e) For the following matrix, find the eigenvalues and also those eigenvectors that corre-spond to the real eigenvalues:21-10 11.5.7 Suppose A is a square matrix and let A be an eigenvalue of A. Prove that if det A±0,then A 0. In this case show that 1/A is an eigenvalue of the inverse A~1.6.1(b,c) Is given matrix diagonalizable? If so, what are the corresponding matrices P and D?1 3 43 10(9)4 0 1() ()1:53 PM2/16/2021

Answered: Image /qna-images/answer/9038215d-9005-4440-b33b-98f7ed95e64a.jpg

Answered: the inverse A 5.1(b,c) Is given matrix…

the inverse A 5.1(b,c) Is given matrix diagonalizable? If so, what are the corresponding matrices P and D? 1 1 0 (9) 1 1 0 (1 3 4 (o) 4 01 3 10 0 0 2

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 70EQ

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Question

Can you help with question 1.6.1.c?

1.4.2 Solve the following systems and determine the number of degrees, of freedom:
0 = Ex+ 7x – IT
0 = Ex – Tx7 + Ix
(a)
X1 + 3x2 + 2x3 +4x4 0
2x1+x2+3x3 = 0
1.4.5 Let a1,.. ., a, be n linearly independent vectors in R". Prove that if a vector b in R" is
orthogonal to all the vectors a1, ., an, then b = 0.
1.5.1(e) For the following matrix, find the eigenvalues and also those eigenvectors that corre-
spond to the real eigenvalues:
21-1
0 1
1.5.7 Suppose A is a square matrix and let A be an eigenvalue of A. Prove that if det A±0,
then A 0. In this case show that 1/A is an eigenvalue of the inverse A~
1.6.1(b,c) Is given matrix diagonalizable? If so, what are the corresponding matrices P and D?
1 3 4
3 10
(9)
4 0 1
() ()
1:53 PM
2/16/2021

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