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