[1 0 -3 Let A = 1 a 1 (a) Find the cofactors C11, C12, C13, C21, C22, C23, C31, C32, C33 of A and use them to construct adj(A), the adjoint of A. (b) Given that det(A) ed v 12 – 3a, explain for which values of a the matrix A is invertible. (c) For the values of a for which A is invertible, use your expression for adj(A) to find A-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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[1 0 -3]
4. Let A =
a
|2 1
6
(a) Find the cofactors C11,
ed vi
C13, C21, C22, C23, C31, C32, C33 of A and use them to construct adj(A),
the adjoint of A.
(b) Given that
= 12 – 3a, explain for which values of a the matrix A is invertible.
(c) For the values of a for which A is invertible, use your expression for adj(A) to find A-1.
Transcribed Image Text:[1 0 -3] 4. Let A = a |2 1 6 (a) Find the cofactors C11, ed vi C13, C21, C22, C23, C31, C32, C33 of A and use them to construct adj(A), the adjoint of A. (b) Given that = 12 – 3a, explain for which values of a the matrix A is invertible. (c) For the values of a for which A is invertible, use your expression for adj(A) to find A-1.
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