a11 a12 is the matrix: a22, (4) The adjugate of a 2 x 2 matrix A a21 a12 a22 adj(A) a11 -a21 A adj (A) det(A)I2. (a) Show that adj(A) A det(A) (b) Show that det(adj(A)) (c) Show that if A is invertible, then A-1= [det(A)]ladj(A)
a11 a12 is the matrix: a22, (4) The adjugate of a 2 x 2 matrix A a21 a12 a22 adj(A) a11 -a21 A adj (A) det(A)I2. (a) Show that adj(A) A det(A) (b) Show that det(adj(A)) (c) Show that if A is invertible, then A-1= [det(A)]ladj(A)
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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please answer only part (c)
![a11
a12
is the matrix:
a22,
(4) The adjugate of a 2 x 2 matrix A
a21
a12
a22
adj(A)
a11
-a21
A adj (A) det(A)I2.
(a) Show that adj(A) A
det(A)
(b) Show that det(adj(A))
(c) Show that if A is invertible, then A-1= [det(A)]ladj(A)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F44884e2d-d01a-4e76-966f-b72e59c96a98%2F0939bc86-f29f-4898-b1aa-3a8f45b36b6b%2Fpjc8ke.jpeg&w=3840&q=75)
Transcribed Image Text:a11
a12
is the matrix:
a22,
(4) The adjugate of a 2 x 2 matrix A
a21
a12
a22
adj(A)
a11
-a21
A adj (A) det(A)I2.
(a) Show that adj(A) A
det(A)
(b) Show that det(adj(A))
(c) Show that if A is invertible, then A-1= [det(A)]ladj(A)
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