Question

Using cofactors of elements of second row, evaluate Δ = \(\begin{vmatrix} 5 & 3 & 8 \\ 2 & 0 & 1 \\ 1 & 2 & 3 \end{vmatrix}\).

Answer 1

Given ∆ = \(\begin{vmatrix} 5 & 3 & 8 \\ 2 & 0 & 1 \\ 1 & 2 & 3 \end{vmatrix}\)

Expanding along R₂

Δ = -2(3 x 3 – 2 x 8) + 0(5 x 3 – 8 x 1)

= -1 (5 x 2 – 3 x 1)

= -2(9 – 16) + 0 – 1(10 – 3)

= -2(-7) – 1(7) = 14 – 7 = 7