Find the minor of 6 and cofactor of 4 respectively in the determinant Δ=| beginmatrix1&2&3 4&5&6 7&8&9 endmatrix|⋅

Question

Find the minor of 6 and cofactor of 4 respectively in the determinant Δ=| beginmatrix1&2&3 4&5&6 7&8&9 endmatrix|⋅ (A) 6, 6 (B) 6, -6 (C) -6 , -6 (D) -6, 6

Tardigrade Admin · Accepted Answer

Minor of 6 = M23=| beginmatrix1&2 7&8 endmatrix|=8-14=-6 Cofactor of 4 = c21=(-1)2+1 | beginmatrix2&3 8&9 endmatrix|=-(18-24)=6

Q. Find the minor of $6$ and cofactor of $4$ respectively in the determinant $Δ = ∣ ∣ 147258369 ∣ ∣ \cdot$

$6, 6$

$6, - 6$

$- 6, - 6$

$- 6, 6$

Minor of $6 = M_{23} = ∣ ∣ 1728 ∣ ∣ = 8 - 14 = - 6$
Cofactor of $4 = c_{21} = (- 1)^{2 + 1} ∣ ∣ 2839 ∣ ∣ = - (18 - 24) = 6$

Q. Find the minor of 6 and cofactor of 4 respectively in the determinant Δ=∣∣​147​258​369​∣∣​⋅

6,6

6,−6

−6,−6

−6,6