Find the cofactors of the element of third row and second column of the following determinant | beginmatrix1&x&y+z 1&y&z+x 1&z&x+y endmatrix|⋅

Question

Find the cofactors of the element of third row and second column of the following determinant | beginmatrix1&x&y+z 1&y&z+x 1&z&x+y endmatrix|⋅ (A) x-y (B) y-x (C) x-z (D) z-x

Tardigrade Admin · Accepted Answer

M32=| beginmatrix1&y+z 1&z+x endmatrix|=z+x-y-z=x-y ⇒ c32=-M32=y-x

Q. Find the cofactors of the element of third row and second column of the following determinant
$∣ ∣ 111 x y z y + z z + x x + y ∣ ∣ \cdot$

$x - y$

$y - x$

$x - z$

$z - x$

$M_{32} = ∣ ∣ 11 y + z z + x ∣ ∣ = z + x - y - z = x - y$
$\Rightarrow c_{32} = - M_{32} = y - x$

Q. Find the cofactors of the element of third row and second column of the following determinant ∣∣​111​xyz​y+zz+xx+y​∣∣​⋅

x−y

y−x

x−z

z−x