Question

If $\left( {1{\text{ }}2{\text{ }}3} \right)B = \left( {3{\text{ }}4} \right)$ then order of matrix $B$ is
A) $3 \times 1$
B) $1 \times 3$
C) $2 \times 3$
D) $3 \times 2$

Answer 1

Here we need to find the order of the matrix. We will use the fact that multiplication of two matrices is possible when the number of columns of the first matrix is equal to the number of rows of the second matrix. Also, the number of columns of the second matrix is equal to the number column of the resultant matrix. Using these we will find the order of the unknown matrix.

Complete step by step solution:
Here it is given that $\left( {1{\text{ }}2{\text{ }}3} \right)B = \left( {3{\text{ }}4} \right)$.
We can see the order of the first matrix is $1 \times 3$ and the order of the resultant matrix is $1 \times 2$.
Let the order of matrices $B$ is $n \times m$.
We know that the multiplication of two matrices is possible when the number of columns of the first matrix is equal to the number of rows.
Therefore, the number of columns of the first matrix is equal to the number of rows of the matrix $B$.
We know, here the number of columns of the first matrix is equal to 3.
Therefore, using this fact, we get
The number of rows of matrix $B$ is equal to 3.
The number of columns of matrix $B$ is equal to the number of columns of the resultant matrix.
Here, the number of columns of the resultant matrix is equal to 2. Therefore, the number of columns of matrix $B$ will be equal to 2.
Hence, the order of matrix $B$ is equal to $3 \times 2$.

Hence, the correct option is option D.

Note:
Here, we have obtained the order of the matrix. A matrix is defined as a collection of numbers which are arranged in columns and rows. The numbers which are used in the matrix are known as the elements of the matrix. Generally, the numbers used in the matrix are real numbers. We should remember that the matrix that has an equal number of rows and columns is called a square matrix.