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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

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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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
Transcribed Image Text: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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