If = | a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 | and A i j is the cofactor of a i j , then the value of is given by:

Question

If $Δ =$ $| \begin{matrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{matrix} |$ and $A_{i j}$ is the cofactor of $a_{i j}$ , then the value of $Δ$ is given by:

Smart Achievers · Accepted Answer

(4)

Ans. $| \begin{matrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{matrix} |$

Explanation:

$∆ =$ sum of the products of the elements of any row (or any column) with their corresponding cofactors.

$∴$ $Δ = a_{11} A_{11} + a_{21} A_{21} + a_{31} A_{31}$

Solution

Q.
If $Δ =$ $| \begin{matrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{matrix} |$ and $A_{i j}$ is the cofactor of $a_{i j}$ , then the value of $Δ$ is given by:

1 $a_{11} A_{31} + a_{12} A_{32} + a_{13} A_{33}$

2 $a_{11} A_{11} + a_{12} A_{21} + a_{13} A_{31}$

3 $a_{21} A_{11} + a_{22} A_{12} + a_{23} A_{13}$

4 $a_{11} A_{11} + a_{21} A_{21} + a_{31} A_{31}$

Ans.
(4)

Ans. $a_{11} A_{11} + a_{21} A_{21} + a_{31} A_{31}$

Explanation:

$∆ =$ sum of the products of the elements of any row (or any column) with their corresponding cofactors.

$∴$ $Δ = a_{11} A_{11} + a_{21} A_{21} + a_{31} A_{31}$

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Solution

Q. If Δ=|a11a12a13a21a22a23a31a32a33| and Aij is the cofactor of aij, then the value of Δ is given by:

1 a11A31+a12A32+a13A33

2 a11A11+a12A21+a13A31

3 a21A11+a22A12+a23A13

4 a11A11+a21A21+a31A31

Ans. (4) Ans. a11A11+a21A21+a31A31 Explanation: ∆= sum of the products of the elements of any row (or any column) with their corresponding cofactors. ∴ Δ=a11A11+a21A21+a31A31