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Question : 6
Total: 29
Given A = [
] , compute A − 1 and show that 2 A − 1 = 9I - A
Solution:
Given A = [
]
|A| = 2 × - [(- 4) × (- 3)] = 2 ⇒A − 1 exist.
Cofactors of matrix A are
C 11 = 7 , C 12 = - 4 , C 21 = - 3 , C 22 = 2
Minors of matrix A are
M 11 = ( − 1 ) 1 + 1 × 7 = 7
M 12 = ( − 1 ) 1 + 2 × (- 4) = 4
M 21 = ( − 1 ) 3 + 1 × (- 3) = 3
M 22 = ( − 1 ) 2 + 2 × 2 = 2
A − 1 =
(
)
2A − 1 = (
) ... (i)
9I - A = 9(
) − (
)
=(
) ... (ii)
⇒2 X − 1 = 9I - A from (i) and (ii)
|A| = 2 × - [(- 4) × (- 3)] = 2 ⇒
Cofactors of matrix A are
Minors of matrix A are
2
9I - A = 9
=
⇒
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