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Question
Find the adjoint of the matrices.
`[(1,-1,2),(2,3,5),(-2,0,1)]`
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Solution
Let A = `[(1,-1,2),(2,3,5),(-2,0,1)]`
Let Cij be cofactors of aij in A.
C11 = `(-1)^(1 + 1) |(3,5),(0,1)|`
= 3 − 0
= 3
C12 = `(-1)^(1 + 2) |(2,5),(-2,1)|`
= −(2 + 10)
= −12
C13 = `(-1)^(1 + 3) |(2,3),(-2,0)|`
= 0 + 6
= 6
C21 = `(-1)^(2 + 1) |(-1,2),(0,1)|`
= −(−1 − 0)
= 1
C22 = `(-1)^(2 + 2) |(1,2),(-2,1)|`
= 1 + 4
= 5
C23 = `(-1)^(2 + 3) |(1,-1),(-2,0)|`
= −(0 − 2)
= 2
C31 = `(-1)^(3 + 1) |(-1,2),(3,5)|`
= −5 − 6
= −11
C32 = `(-1)^(3 + 2) |(1,2),(2,5)|`
= −(5 − 4)
= −l
C33 = `(-1)^(3 + 3) |(1,-1),(2,3)|`
= 3 + 2
= 5
∴ Adj A `= [(C_11,C_12,C_13),(C_21,C_22,C_23),(C_31,C_32,C_33)]^T`
= `[(3,-12,6),(1,5,2),(-11,-1,5)]^T`
= `[(3,1,-11),(-12,5,-1),(6,2,5)]`
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