CBSE Class 12 Math 2018 Solved Paper

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Question : 6
Total: 29
Given A = [
23
47
]
, compute A1 and show that 2 A1 = 9I - A
Solution:  
Given A = [
23
47
]

|A| = 2 × - [(- 4) × (- 3)] = 2 ⇒ A1 exist.
Cofactors of matrix A are
C11 = 7 , C12 = - 4 , C21 = - 3 , C22 = 2
Minors of matrix A are
M11 = (1)1+1 × 7 = 7
M12 = (1)1+2 × (- 4) = 4
M21 = (1)3+1 × (- 3) = 3
M22 = (1)2+2 × 2 = 2
A1 =
1
2
(
73
42
)

2 A1 = (
73
42
)
... (i)
9I - A = 9 (
10
01
)
(
23
47
)

= (
73
42
)
... (ii)
2X1 = 9I - A from (i) and (ii)
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