If the matrix $\displaystyle \ \begin{bmatrix}a & 2b-c\\ 2a+d 2c-4\end{bmatrix}$ is a null matrix then find the values of a, b, c and d.

Given :

The given matrix $\displaystyle \ \begin{bmatrix} a & 2b-c\\ 2a+d & 2c-4 \end{bmatrix}$ is a null matrix.

To find :

We have to find the values of a, b, c and d.

Solution :

Null matrix:

A zero matrix or null matrix is a matrix all of whose entries are zero.

Therefore,

$\begin{bmatrix}
a & 2b-c\\
2a+d & 2c-4
\end{bmatrix} =\begin{bmatrix}
0 & 0\\
0 & 0
\end{bmatrix}$  

This implies

$a = 0$  ----(1)

$2b-c = 0$ ----(2)

$2a+d = 0$

$2(0)+d = 0$

$d =0$

$2c-4 = 0$

$2c = 4$

$c = \frac{4}{2}$

$c = 2$

Substitute c = 2 in equation (2)

$2b-2 =0$

$2b = 2$

$b = \frac{2}{2}$

$b = 1$.

Therefore, 

a=0, b=1, c=2 and d=0.

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

42 Views

Kickstart Your Career

Get certified by completing the course

Get Started