Problem 1. Let 4 0 0 0. -1 2 0 -1 5 2 6. 13 1 5 2 ,D = 3 A = 1 0. ,E = 1 3 1 6. 0 7 -3 0 2 4 1 3 10 2 4 1 (e) det(D) (f) det(D"(4E")– 4(ED)") | (g) det(B-1)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Problem 1. Let
0 0
-1 2 0
1 5
6.
4
1 3
-1 1 2
1 3
152
6.
|
(: :).c=
1 5 2
D
3 1 5
A =
0 1
2 4
B
1
E
%3D
6 2
0 7
-3 0
3
10
2 4
1
(e) det(D)
(f) det(D"(4E")– 4(ED)")
(g) det(B-1)
(h) det(¿A)
Transcribed Image Text:Problem 1. Let 0 0 -1 2 0 1 5 6. 4 1 3 -1 1 2 1 3 152 6. | (: :).c= 1 5 2 D 3 1 5 A = 0 1 2 4 B 1 E %3D 6 2 0 7 -3 0 3 10 2 4 1 (e) det(D) (f) det(D"(4E")– 4(ED)") (g) det(B-1) (h) det(¿A)
Problem 2. Suppose that A is an n x n matrix and det(A) = 2, det(A+ I) = 3, and
det (A + 21) = 5. Compute the following.
(a) det(Aª + 3A³ + 2A²)
(b) det(-A°(A+ I)*)
(c) det(3A"(A+ 21)-1)
Transcribed Image Text:Problem 2. Suppose that A is an n x n matrix and det(A) = 2, det(A+ I) = 3, and det (A + 21) = 5. Compute the following. (a) det(Aª + 3A³ + 2A²) (b) det(-A°(A+ I)*) (c) det(3A"(A+ 21)-1)
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