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Question
Write Minors and Cofactors of the elements of following determinants:
`|(1,0,4),(3,5,-1),(0,1,2)|`
Solution
Minors:
`M_11 = abs ((5,-1),(1,2)) = 5 xx 2 - 1 = 11`
`M_12 abs ((3,-1),(0,2)) = 3 xx 2 - 0 = 6`
`M_13 = abs ((3,5),(0,1)) = 3 xx 1 - 0 = 3`
`M_21 abs ((0,4),(1,2)) = 0 xx 2 - 1 xx 4 = - 4`
`M_22 = abs ((1,4),(0,2)) = 1 xx 2 - 0 = 2`
`M_23 = abs ((1,0),(0,2))= 1 xx 1 = 1`
`M_31 = |(0,4), (5, -1)| = -20`
`M_32 = abs ((1,4),(3,-1)) = 1 xx -(1) - 3 xx 4 = 13`
`M_33 = abs ((1,0),(3,5)) = 5 - 0 = 5`
Cofactors:
`A_11 = (- 1)^(1 + 1) M_11 = 11`
`A_12 = (-1)^(1 + 2) M_12 = (-1) xx 6 = -6`
`A_13 = (-1)^(1 + 3) M_12 = 1 * 3 = 3`
`A_21 = (-1)^(2 + 1) M_21 = (-1) xx (-4) = 4`
`A_22 = (-1)^(2 + 2) M_22 = 1 xx 2 = 2`
`A_23 = (-1)^(2 + 3) M_23 = (-1) * 1 = -1`
`A_31 = (-1)^(3 + 1) M_31 = 1 * (- 20) = - 20`
`A_32 = (-1)^(3 + 2) M_32 = (-1)(- 13) = 13`
`A_33 = (-1)^(3 + 3) M_33 = 1*5 = 5`
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