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Question
Find the matrix of the co-factor for the following matrix.
`[(1,3),(4,-1)]`
Solution
Let A = `[(1,3),(4,-1)]`
Here, a11 = 1, M11 = − 1
∴ A11 = (− 1)1+1(− 1) = − 1
a12 = 3, M12 = 4
∴ A12 = (− 1)1+2(4) = − 4
a21 = 4, M21 = 3
∴ A21 = (− 1)2+1(3) = − 3
a22 = − 1, M22 = 1
∴ A22 = (− 1)2+2(1) = 1
∴ the co-factor matrix = `[("A"_11,"A"_12),("A"_21,"A"_22)]`
= `[(-1,-4),(-3,1)]`
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