Question

If A = `[(1, 2, 3),(1, 1, 5),(2, 4, 7)]`, then find the value of a₃₁A₃₁ + a₃₂A₃₂ + a₃₃A₃₃.

Answer 1

We have,

A = `[(1, 2, 3),(1, 1, 5),(2, 4, 7)]`

a₃₁ = 2, a₃₂ = 4, a₃₃ = 7

A₃₁ = `|(2, 3),(1, 5)|` = 10 - 3 = 7

A₃₂ = `- |(1, 3),(1, 5)|` = - (5 - 3) = - 2

A₃₃ = `|(1, 2),(1, 1)|` = 1 - 2 = - 1

∴ a₃₁A₃₁ + a₃₂A₃₂ + a₃₃A₃₃ 

= 2(7) + 4(-2) + 7(-1)

= 14 - 8 - 7 

= - 1