Question

The product of `A = [(1, -2),(-3, 4)]` and matrix M, AM = B where `B = [(2), (24)]`, then the order of matrix M is ______.

Options

• 2 × 2

• 2 × 1

• 1 × 2

• 4 × 1

Answer 1

The product of `A = [(1, -2),(-3, 4)]` and matrix M, AM = B where `B = [(2),(24)]`, then the order of matrix M is 2 × 1.

Explanation:

Let M be of order a × b.

A is 2 × 2, so AM is defined only if the number of columns of A (2) equals the number of rows of M, hence a = 2. 

The product AM then has order 2 × b, but B is 2 × 1, so b = 1.

Therefore, M is 2 × 1.