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प्रश्न
Find the adjoint of the following matrix.
`[(1, -1, 2),(-2, 3, 5),(-2, 0, -1)]`
उत्तर
Let A = `[(1, -1, 2),(-2, 3, 5),(-2, 0, -1)]`
Now, M11 = `|(3, 5),(0, -1)|` = −3 − 0 = −3
∴ A11 = (−1)1+1(− 3) = −3
M12 = `|(-2, 5),(-2, -1)|` = 2 + 10 = 12
∴ A12 = (−1)1+2(12) = −12
M13 = `|(-2, 3),(-2, 0)|` = 0 + 6 = 6
∴ A13 = (− 1)1+3(6) = 6
M21 = `|(-1,2),(0,-1)|` = 1 − 0 = 1
∴ A21 = (−1)2+1(1) = −1
M22 = `|(1, 2),(-2, -1)|` = −1 + 4 = 3
∴ A22 = (−1)2+2(3) = 3
M23 = `|(1, -1),(-2, 0)|` = 0 − 2 = −2
∴ A23 = (−1)2+3(−2) = 2
M31 = `|(-1, 2),(3, 5)|` = −5 − 6 = −11
∴ A31 = (−1)3+1(−11) = −11
M32 = `|(1, 2),(-2, 5)|` = 5 + 4 = 9
∴ A32 = (−1)3+2(9) = −9
M33 = `|(1, -1),(-2, 3)|` = 3 − 2 = 1
∴ A33 = (−1)3+3(1) = 1
The co-factor matrix = `[("A"_11, "A"_12, "A"_13),("A"_21, "A"_22, "A"_23),("A"_31, "A"_32, "A"_33)]`
∴ adj A = `[(-3, -12, 6),(-1, 3, 2),(-11, -9, 1)]^"T"`
= `[(-3, -1, -11),(-12, 3, -9),(6, 2, 1)]`
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