Let 6 -2 3 -5 A = -2 and B = 2 -3 (a) Find AB, A-1, and B-1. 14 -24 AB = -4 7 1/2 A-1 %3D 1 3 -3 B-1 %3D -2 3 (b) Show that (AB)-1 = B¬1A-1, 24 (AB)-1 %3D 14

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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Let
6-2
3 -5
A =
and B =
-2
2 -3|
(a) Find AB, A-1, and B-1.
14
-24
AB =
-4
7
1/2
1
A-1
1
3
-3
5
B-1
-2
3.
(b) Show that (AB)-1 = B-1a-1.
24
(AB)–1
!!
4
14
24
B-A-1
%3D
4
14
1个
Transcribed Image Text:Let 6-2 3 -5 A = and B = -2 2 -3| (a) Find AB, A-1, and B-1. 14 -24 AB = -4 7 1/2 1 A-1 1 3 -3 5 B-1 -2 3. (b) Show that (AB)-1 = B-1a-1. 24 (AB)–1 !! 4 14 24 B-A-1 %3D 4 14 1个
1/2
A-1
-3
-2
(b) Show that (AB)¯1 = B¯'A1.
%3D
24
(AB)¬1
%3D
4
14
7
24
B-'A¬1 =
4.
14
3.
Transcribed Image Text:1/2 A-1 -3 -2 (b) Show that (AB)¯1 = B¯'A1. %3D 24 (AB)¬1 %3D 4 14 7 24 B-'A¬1 = 4. 14 3.
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