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Question
Find the adjoint of the following matrices : `[(2, -3),(3, 5)]`
Solution
Let A = `[(2, -3),(3, 5)]`
Here,
a11 = 2
∴ M11 = 5 and A11 = (– 1)1+1 (5) = 5
a12 = – 3
∴ M12 = 3 and A12 = (– 1)1+2 (3) = – 3
a21 = 3
∴ M21 = – 3 and A21 = (– 1)2+1 (– 3) = 3
a22 = 5
∴ M22 = 2 and A22 = (– 1)2+2 (2) = 2
∴ The matrix of the co-factors is
[Aij]2x2 = `[("A"_11, "A"_12),("A"_21, "A"_22)] = [(5, -3),(3, 2)]`
Now, adj A = `["A"_"ij"]_(2xx2)^"T" = [(5, 3),(-3, 2)]`.
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