If D=|a11 a12 a21 a22| and corresponding cofactors of elements be written as c11, c12, c21 and c22, then the value of a 11 c 21+ a 12 c 22+ a 21 c 11+ a 22 c 12 is equal to

Question

If D=|a11 a12 a21 a22| and corresponding cofactors of elements be written as c11, c12, c21 and c22, then the value of a 11 c 21+ a 12 c 22+ a 21 c 11+ a 22 c 12 is equal to (A) 0 (B) D (C) 2 D (D) - D

Tardigrade Admin · Accepted Answer

Θ a11 c21+a12 c22=0 text and a21 c11+a22 c12=0 ∴ text sum =0

Q. If $D = ∣ ∣ a_{11} a_{21} a_{12} a_{22} ∣ ∣$ and corresponding cofactors of elements be written as $c_{11}, c_{12}, c_{21}$ and $c_{22}$ , then the value of $a_{11} c_{21} + a_{12} c_{22} + a_{21} c_{11} + a_{22} c_{12}$ is equal to

0

$D$

$2 D$

$- D$

$Θ a_{11} c_{21} + a_{12} c_{22} = 0$
$and a_{21} c_{11} + a_{22} c_{12} = 0$
$∴ sum = 0$

Q. If D=∣∣​a11​a21​​a12​a22​​∣∣​ and corresponding cofactors of elements be written as c11​,c12​,c21​ and c22​, then the value of a11​c21​+a12​c22​+a21​c11​+a22​c12​ is equal to

0

D

2D

−D

Θa11​c21​+a12​c22​=0 and a21​c11​+a22​c12​=0 ∴ sum =0

Q. If $D = ∣ ∣ a_{11} a_{21} a_{12} a_{22} ∣ ∣$ and corresponding cofactors of elements be written as $c_{11}, c_{12}, c_{21}$ and $c_{22}$ , then the value of $a_{11} c_{21} + a_{12} c_{22} + a_{21} c_{11} + a_{22} c_{12}$ is equal to

$D$

$2 D$

$- D$

$Θ a_{11} c_{21} + a_{12} c_{22} = 0$
$and a_{21} c_{11} + a_{22} c_{12} = 0$
$∴ sum = 0$