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If  \(\Delta=\left|\begin{array}{lll} {a_{11}} & {a_{12}} & {a_{13}} \\ {a_{21}} & {a_{22}} & {a_{23}} \\ {a_{31}} & {a_{32}} & {a_{33}} \end{array}\right|\) and Aij is Cofactors of aij, then the value of \(\Delta\) is given by
  • a11 A31 + a12 A32 + a13 A33
  • a21 A11 + a22 A12 + a23 A13
  • a11 A11 + a21 A21 + a31 A31
  • a11 A11 + a12 A21 + a13 A31
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If  \(\Delta=\left|\begin{array}{lll} {a_{11}} & {a_{12}} & {a_{13}} \\ {a_{21}} & {a_{22}} & {a_{23}} \\ {a_{31}} & {a_{32}} & {a_{33}} \end{array}\right|\) and Aij is Cofactors of aij, then the value of \(\Delta\) is given by
  • a11 A31 + a12 A32 + a13 A33
  • a21 A11 + a22 A12 + a23 A13
  • a11 A11 + a21 A21 + a31 A31
  • a11 A11 + a12 A21 + a13 A31

Answer

\(\Delta=\left|\begin{array}{lll} {a_{11}} & {a_{12}} & {a_{13}} \\ {a_{21}} & {a_{22}} & {a_{23}} \\ {a_{31}} & {a_{32}} & {a_{33}} \end{array}\right|\)
Expanding along Column 1
\(\Delta=(-1)^{1+1} \times a_{11} \times\left|\begin{array}{ll} {a_{22}} & {a_{23}} \\ {a_{32}} & {a_{33}} \end{array}\right|\) + \((-1)^{2+1} \times a_{21} \times\left|\begin{array}{ll} {a_{12}} & {a_{13}} \\ {a_{32}} & {a_{33}} \end{array}\right|\) + \((-1)^{3+1} \times a_{31} \times\left|\begin{array}{ll} {a_{12}} & {a_{13}} \\ {a_{22}} & {a_{23}} \end{array}\right|\)
\(\Delta\) = a11A11 + a21A21 + a31A31
Therefore the choice is: C
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