Name: Multiplication of a Matrix by a Scalar
Uploaded: 2019-07-19
Duration: 2 min 12 s
Description: Can we multiply the scalar with the matrix? Yes, in scalar multiplication, each entry in the matrix is multiplied by the given scalar. Watch to learn more.

Question

Write the order of the following matrix.

$A = [\begin{matrix} 3 & 1 \\ 1 & 2 \end{matrix}]$

Also, find the elements $a_{21}$ and $a_{22}$ . Show that $a_{11} \times a_{22} = 3 (a_{12} + a_{21})$ .

Accepted Answer

Given matrix is $A = [\begin{matrix} 3 & 1 \\ 1 & 2 \end{matrix}]$ .

A matrix having $m$ rows and $n$ columns is called a matrix of order $m \times n$ and read as ' $m$ by $n$ '. By convention, number of rows are listed first and columns, second.

Since matrix $A$ has two rows and two columns.

Therefore, the order of matrix $A$ is $2 \times 2$ .

Also, the numbers, symbols, or expressions in the matrix are called its entries or its elements. The horizontal and vertical lines of entries in a matrix are called rows and columns, respectively.

The element $a_{i j}$ belongs to $i^{t h}$ row and $j^{t h}$ column and it is called ${(i, j)}^{t h}$ element of the matrix $A = [a_{i j}]$ .

Here, element $a_{11} = 3, a_{12} = 1, a_{21} = 1$ and $a_{22} = 2$ .

Now, $a_{11} \times a_{22} = 3 (a_{12} + a_{21})$

Here, $L H S = a_{11} \times a_{22} = 3 \times 2 = 6$ .

and $R H S = 3 (a_{12 +} a_{21}) = 3 (1 + 1) = 3 \times 2 = 6 = L H S$

Hence, proved.

Write the order of the following matrix.

$A = [\begin{matrix} 3 & 1 \\ 1 & 2 \end{matrix}]$

Also, find the elements $a_{21}$ and $a_{22}$ . Show that $a_{11} \times a_{22} = 3 (a_{12} + a_{21})$ .

Important Questions on Matrices

Learn and Prepare for any exam you want !

Write the order of the following matrix. A=3112 Also, find the elements a21and a22. Show that a11×a22=3a12+a21.

Important Questions on Matrices

Learn and Prepare for any exam you want !

Write the order of the following matrix.

$A = [\begin{matrix} 3 & 1 \\ 1 & 2 \end{matrix}]$

Also, find the elements $a_{21}$ and $a_{22}$ . Show that $a_{11} \times a_{22} = 3 (a_{12} + a_{21})$ .