Q7Let A be a 4 x 4 matrix with eigenvalues:d1 = v3 with corresponding eigenvectors [3t, t, –8t, 2t), teR, t+0.1with corresponding eigenvectors [5r, 3r, r, 0], re R, r+0.%3D23pA3 = 14 = 0 with corresponding eigenvectors2g,P, q, p,q E R, not both 0.2Answer the following questions:а)Is the matrix A an invertible matrix. Justify.b)Is the matrix A a diagonalizable matrix. Justify.c)Find an invertible matrix P and a diagonal matrix D that satisfy P 'AP = D.

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Q7 Let A be a 4 x 4 matrix with eigenvalues: d1 = v3 with corresponding eigenvectors [3t, t, -8t, 2t], te R, t+0. A2 = with corresponding eigenvectors [5r, 3r, r, 0], re R, r+0. 3p 2q A3 = A4 = 0 with corresponding eigenvectors + P, q E R, not both 0. -- Answer the following questions: a) Is the matrix A an invertible matrix. Justify. b) Is the matrix A a diagonalizable matrix. Justify. c) Find an invertible matrix P and a diagonal matrix D that satisfy P'AP = D.

Q7 Let A be a 4 x 4 matrix with eigenvalues: d1 = v3 with corresponding eigenvectors [3t, t, -8t, 2t], te R, t+0. A2 = with corresponding eigenvectors [5r, 3r, r, 0], re R, r+0. 3p 2q A3 = A4 = 0 with corresponding eigenvectors + P, q E R, not both 0. -- Answer the following questions: a) Is the matrix A an invertible matrix. Justify. b) Is the matrix A a diagonalizable matrix. Justify. c) Find an invertible matrix P and a diagonal matrix D that satisfy P'AP = D.

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

Q7
Let A be a 4 x 4 matrix with eigenvalues:
d1 = v3 with corresponding eigenvectors [3t, t, –8t, 2t), teR, t+0.
1
with corresponding eigenvectors [5r, 3r, r, 0], re R, r+0.
%3D
2
3p
A3 = 14 = 0 with corresponding eigenvectors
2g
,P, q, p,q E R, not both 0.
2
Answer the following questions:
а)
Is the matrix A an invertible matrix. Justify.
b)
Is the matrix A a diagonalizable matrix. Justify.
c)
Find an invertible matrix P and a diagonal matrix D that satisfy P 'AP = D.

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