1.

If Δ=\(\begin{vmatrix}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33} \end{vmatrix}\), then the determinant in terms of cofactors Aij can be expressed as a11 A11+a21 A21+a31 A31.(a) True(b) FalseI have been asked this question in an online quiz.This key question is from Determinants topic in chapter Determinants of Mathematics – Class 12

Answer»

Right answer is (a) True

To EXPLAIN I would say: The given STATEMENT is true.

Expanding the determinant Δ=\(\begin{vmatrix}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33} \end{vmatrix}\) along R1, we get

Δ=(-1)^1+1 a11 \(\begin{vmatrix}a_{22}&a_{23}\\a_{32}&a_{33} \end{vmatrix}\)+(-1)^1+2 a12 \(\begin{vmatrix}a_{21}&a_{23}\\a_{31}&a_{33} \end{vmatrix}\)+(-1)^1+3 a13 \(\begin{vmatrix}a_{21}&a_{22}\\a_{31}&a_{32} \end{vmatrix}\)

Δ=a11 A11+a21 A21+A31 A31, where AIJ is the cofactor of aij.


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