Question

Let A `[(1, -2, -1), (0, 4, -1), (-3, 2, 1)]`, B = `[(-2), (-5), (-7)]`, C = [9 8 7], which of the following is defined?

Options

• Only AB

• Only AC

• Only BA

• All AB, AC, and BA

Answer 1

Only AB

Explanation:

A = `[(1, -2, -1), (0, 4, -1), (-3, 2, 1)]_(3 xx 3)`

B = `[(-2), (-5), (-7)]_(3 xx 1)`

C = [9 8 7]_1×3

For AB

⇒ Number of columns matrix A (3) = Number of row matrix B (3)

So, AB is defined.

For BA

⇒ Number of columns matrix B (1) ≠ Number of row of matrix A (3).

BA is not defined.

For AC

⇒ Number of columns matrix A(3) ≠ Number of row of matrix C (1). 

So, AC is not defined.

Only AB is defined.