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InterviewSolution
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Write the minor and cofactor of each element of the following determinants and also evaluate the determinant in each case: ` |[1,3,-2],[4,-5,6],[3,5,2]| ` |
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Answer» The minors of the elements of `Delta` are given by `M_(11) = |{:(-1, 2), (5, 2):}| =-12, M_(12) = |{:(4, 2), (3, 2):}| = 2, M_(13) = |{:(4, -1), (3, 5):}| =23,` `M_(21) = |{:(-3, 2), (5, 2):}| =-16, M_(22) = |{:(1, 2), (3, 2):}| = -4, M_(23) = |{:(1, -3), (3, 5):}| =14,` `M_(31) = |{:(-3, 2), (-1, 2):}| =-4, M_(32) = |{:(1, 2), (4, 2):}| = -6, M_(33) = |{:(1, -3), (4, -1):}| =11` So, the cofactors of the corresponding elements of `Delta` are `C_(11) = (-1)^(1+1) * M_(11) = M_(11) = -12, C_(12) = (-1)^(1+2) * M_(12) = -M_(12) = -2,` `C_(13) = (-1)^(1+3) * M_(13) = M_(13) = 23, C_(21) = (-1)^(2+1) * M_(21) = -M_(21) = 16,` `C_(22) = (-1)^(2+2) * M_(22) = M_(22) = -4, C_(23) = (-1)^(2+3) * M_(23) = -M_(23) = -14,` `C_(31) = (-1)^(3+1) * M_(31) = M_(31) = -4, C_(32) = (-1)^(3+2) * M_(32) = -M_(32) = 6,` `C_(33) = (-1)^(3+3) * M_(33) = M_(33) = 11`. |
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