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# Question and Answer

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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## QuestionMathsClass 12

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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