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Question
Find the cofactor matrix, of the following matrices : `[(1, 2),(5, -8)]`
Solution
The co-factor Aij of aij is equal to (– 1)i+j Mij.
Here,
a11 = 1
∴ M11 = – 8
and A11 = (– 1)1+2 M11 = (1) (– 8) = – 8
a12 = 2
∴ M11 = 5
and A12 = (– 1)1+2 M12 = (– 1) (5) = – 5
a21 = 5
∴ M21 = 2
and A21 = (– 1)2+1 M21 = (– 1) (2) = – 2
a22 = – 8
∴ M22 = 1
and A22 = (– 1)2+2 M22 = (1) (1) = 1
∴ The matrix of the co-factors is
[Aij]2x2 = `[("A"_11, "A"_12),("A"_21, "A"_22)]`
= `[(-8, -5),(-2, 1)]`.
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