For each of the following matrices A₁, where i = 1 or 2, find an invertible matrix P; and a diagonal matrix D; such that A; = P;D;P;¯¯ 1 -1 -4 -4 4 0 4 (a) A₁ = P₁ = 0 D₁ = 0 0 0 -1 0 0 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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For each of the following matrices Aį, where i = 1 or 2, find an invertible matrix P₁ and a diagonal matrix D₂ such that A₂ = P;D;P;¯¹.
-1
(a) A1₁
P₁ =
=
(b) A₂ =
P₂ =
-1
-4
0
−1 4
-4 4
0 4
-4 -12 4
-2 -6 2
4 12
AN
D₁
D₂ =
0
0
0
0
0
0
0
0
0
0
0
0
Transcribed Image Text:For each of the following matrices Aį, where i = 1 or 2, find an invertible matrix P₁ and a diagonal matrix D₂ such that A₂ = P;D;P;¯¹. -1 (a) A1₁ P₁ = = (b) A₂ = P₂ = -1 -4 0 −1 4 -4 4 0 4 -4 -12 4 -2 -6 2 4 12 AN D₁ D₂ = 0 0 0 0 0 0 0 0 0 0 0 0
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