Question

Given that A = [a_ij] is a square matrix of order 3 × 3 and |A| = −7, then the value of `sum_("i" = 1)^3 "a"_("i"2)"A"_("i"2)`, where A_ij denotes the cofactor of element a_ij is:

Options

• 7

• −7

• 0

• 49

Answer 1

−7

Explanation:

|A| = −7

∴ `sum_("i" = 1)^3 "a"_("i"2)"A"_("i"2)` = a₁₂A₁₂ + a₂₂A₂₂ + a₃₂A₃₂ = |A| = −7