20 1 Consider the matrix A = 01 0 0 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 x2 x3] 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).)

20 1 Consider the matrix A = 01 0 0 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 x2 x3] 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).)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.7: The Inverse Of A Matrix

Problem 30E

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