(a) Show that if D is a diagonal matrix with nonnegative en- tries on the main diagonal, then there is a matrix S such that S² = D. (b) Show that if A is a diagonalizable matrix with nonnegative eigenvalues, then there is a matrix S such that S² = A. (c) Find a matrix S such that S² = A, given that 1 3 A = 0 4 5 0 0 9
(a) Show that if D is a diagonal matrix with nonnegative en- tries on the main diagonal, then there is a matrix S such that S² = D. (b) Show that if A is a diagonalizable matrix with nonnegative eigenvalues, then there is a matrix S such that S² = A. (c) Find a matrix S such that S² = A, given that 1 3 A = 0 4 5 0 0 9
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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Transcribed Image Text:(a) Show that if D is a diagonal matrix with nonnegative en-
tries on the main diagonal, then there is a matrix S such
that S² = D.
(b) Show that if A is a diagonalizable matrix with nonnegative
eigenvalues, then there is a matrix S such that S² = A.
(c) Find a matrix S such that S² = A, given that
1 3
A =
0
4
5
0
0
9
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