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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
Solution
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
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