Question

If A = `[(1, 2, 1), (3, 2, 3), (2, 1, 2)]`, then `a_11A_11 + a_21A_21 + a_31A_31` = ______ 

Options

• 1

• 2

• |A|

• 3

Answer 1

If A = `[(1, 2, 1), (3, 2, 3), (2, 1, 2)]`, then `a_11A_11 + a_21A_21 + a_31A_31` = |A|

Explanation:

`a_11A_11 + a_21A_21 + a_31A_31`

= 1(4 - 3) + 3[-1(4 - 1)] + 2(6 - 2) = 0

and |A| = 1(4 - 3) - 2(6 - 6) + 1(3 - 4) = 0

∴ `a_11A_11 + a_21A_21 + a_31A_31` = |A|