Question

Find the value of determinant expanding along third column

`|(-1, 1, 2),(-2, 3, -4),(-3, 4, 0)|`

Answer 1

Here, `|("a"_11, "a"_12, "a"_13),("a"_21, "a"_22, "a"_23),("a"_31, "a"_32, "a"_33)| = |(-1, 1, 2),(-2, 3, -4),(-3, 4, 0)|`

Expansion along the third column

= a₁₃ C₁₃ + a₂₃ C₂₃ + a₃₃ C₃₃

= `2 xx (-1)^(1 + 3) |(-2, 3),(-3, 4)| -4 xx (-1)^(2 + 3)|(-1, 1),(-3, 4)| + 0 xx (-1)^(3 + 3)|(-1, 1),(-2, 3)|`

= 2 (– 8 + 9) + 4 (– 4 + 3) + 0

= 2 – 4

= – 2