Consider the matrix A = 2 0 1 010 02 a) Diagonalize the symmetric matrix A = SAST, i.e. compute the eigenvalue decomposition. b) Using the eigenvalue decomposition, compute 1) the determinant of the matrix A. 2) the rank of the matrix A. 3) the inverse matrix A-¹. c) Decompose the quadratic form Q(x) = x² Ax with x = [*₁ 22 23] as the sum of r = rank(A) squares of independent linear forms. (Note: different solutions exist, one is sufficient! Either use the elimination method or the eigenvalue decomposition computed in a).)
Consider the matrix A = 2 0 1 010 02 a) Diagonalize the symmetric matrix A = SAST, i.e. compute the eigenvalue decomposition. b) Using the eigenvalue decomposition, compute 1) the determinant of the matrix A. 2) the rank of the matrix A. 3) the inverse matrix A-¹. c) Decompose the quadratic form Q(x) = x² Ax with x = [*₁ 22 23] as the sum of r = rank(A) squares of independent linear forms. (Note: different solutions exist, one is sufficient! Either use the elimination method or the eigenvalue decomposition computed in a).)
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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Question
7.3
![Consider the matrix A =
0
1
a) Diagonalize the symmetric matrix A = SAST, i.e. compute the eigenvalue decomposition.
b) Using the eigenvalue decomposition, compute
1) the determinant of the matrix A.
2) the rank of the matrix A.
3) the inverse matrix A-¹.
rank(A)
c) Decompose the quadratic form Q(x) = x² Ax with x = = [*₁ x2 *3] as the sum of r =
squares of independent linear forms. (Note: different solutions exist, one is sufficient! Either
use the elimination method or the eigenvalue decomposition computed in a).)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd6070c27-0824-4884-a918-195c8f609349%2Fa7866182-daa8-4a40-97ee-9afd83a32688%2F0xcqt5_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the matrix A =
0
1
a) Diagonalize the symmetric matrix A = SAST, i.e. compute the eigenvalue decomposition.
b) Using the eigenvalue decomposition, compute
1) the determinant of the matrix A.
2) the rank of the matrix A.
3) the inverse matrix A-¹.
rank(A)
c) Decompose the quadratic form Q(x) = x² Ax with x = = [*₁ x2 *3] as the sum of r =
squares of independent linear forms. (Note: different solutions exist, one is sufficient! Either
use the elimination method or the eigenvalue decomposition computed in a).)
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