Question

What is the order of \(\begin{bmatrix} 2\\ 4\\ 6\end{bmatrix} \begin{bmatrix} x & 5 & 6 \end{bmatrix}\)?
1.  3 × 3
2.  1 × 3
3.  1 × 1
4.  3 × 1
5. 2 × 3

Answer 1

Correct Answer - Option 1 :  3 × 3

Concept:

Order of a matrix is determined by the number of rows and columns the matrix consists.

To multiply an m × n matrix by an n × p matrix, the n must be the same, and the result is an m × p matrix.
Calculation:

We have to find the order of \(\begin{bmatrix} 2\\ 4\\ 6\end{bmatrix} \begin{bmatrix} x & 5 & 6 \end{bmatrix}\)

Let \(\begin{bmatrix} 2\\ 4\\ 6\end{bmatrix} \begin{bmatrix} x & 5 & 6 \end{bmatrix}\)

Order of matrix A is (3 × 1)

Order of matrix B is (1 × 3)

Now, Order of A (3 × 1) B (1 × 3) is (3 × 3)

So, Order of AB = (3 × 3)

∴  Option 1st is the correct answer.