Question

If `M xx [(3, 2),(-1, 0)] = [(3, -1)]`, the order of matrix M is ______.

Options

• 2 × 2

• 2 × 1

• 1 × 2

• 1 × 3

Answer 1

If `M xx [(3, 2),(-1, 0)] = [(3, -1)]`, the order of matrix M is 1 × 2.

Explanation:

Order of matrix on R.H.S = 1 × 2

Let M be a matrix of order m × n

And N = `[(3, 2),(-1, 0)]` is a matrix of order 2 × 2

Since MN = `[(3, -1)]_(1 xx 2)`

Now MN exists

If No. of columns in M = No. of rows in N

`\implies` n = 2

∴ MN is a matrix of order m × 2

`\implies` m = 1

Thus, M is a matrix of order m × n i.e. 1 × 2