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Question
The adjoint matrix of `[(3, -3, 4),(2, -3, 4),(0, -1, 1)]` is ______.
Options
`[(4, 8, 3),(2, 1,6),(0, 2, 1)]`
`[(1, -1, 0),(-2, 3, -4),(-2, 3, -3)]`
`[(11, 9, 3),(1, 2, 8),(6, 9, 1)]`
`[(1, -2, 1),(-1, 3, 3),(-2, 3, -3)]`
Solution
The adjoint matrix of `[(3, -3, 4),(2, -3, 4),(0, -1, 1)]` is `bbunderline([(1, -1, 0),(-2, 3, -4),(-2, 3, -3)])`.
Explanation:
`M_11 = |(-3, 4), (-1, 1) = -3 + 4 = 1|`
`M_12 = |(2, 4), (0, 1)| = 2 + 0 = 2`
`M_13 = |(2, -3), (0, -1)| = -2 + 0 = -2`
`M_21 = |(-3, -1), (-1, 1)| = -3 + 4 = 1`
`M_22 = |(3, 4), (0, 1)| = 3 - 0 = 3`
`M_23 = |(3, -3), (0, -1)| = -3 + 0 = 3`
`M_31 = |(-3, 4), (-3, 4)| = 12 - 8 = 4`
`M_32 = |(3, 4), (2, 4)| = 12 - 8 = 4`
`M_33 = |(3, -3), (2, -3)| = -9 + 6 = 3`
A11 = −1
A12 = −2
A13 = −2
A21 = −1
A22 = 3
A23 = 3
A31 = 0
A32 = −4
A33 = −3
[Cofactor A] = `[(-1, -2, -2), (-1, 3, 3), (0, -4, -3)]`
Adj (A) = (Cof A)T
`[(-1, -1, 0), (-2, 3, -4), (-2, 3, -3)]`
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