Browse Questions

# Find the values of x and y make the following pairs of matrices equal : $\begin{bmatrix} 3x+6 & 5 \\ y+1 & 2-x \end{bmatrix} = \begin{bmatrix} 0 & y-2 \\ 8 & 4 \end{bmatrix}$

Toolbox:
• If the order of 2 matrices are equal, their corresponding elements are equal, i.e, if $A_{ij}=B_{ij}$, then any element $a_{ij}$ in matrix A is equal to corresponding element $b_{ij}$ in matrix B.
• We can then match the corresponding elements and solve the resulting equations to find the values of the unknown variables.
Step1:
Given
$\begin{bmatrix} 3x+6 & 5 \\ y+1 & 2-x \end{bmatrix} = \begin{bmatrix} 0 & y-2 \\ 8 & 4 \end{bmatrix}$
The given matrices are equal hence their corresponding elements should be equal.
3x+6=0-----(1)
y-2=5------(2)
y+1=8-----(3)
2-x=4------(4)
From equation (4) we have
2-x=4
-x=2
x= - 2.
Step2:
From equation (1) we have
3x+6=0
3x=-6
$x=-\frac{6}{3}$
x= - 2.
Step3:
From equation (2) we have
y-2=5
y=5+2
y=7
Step4:
From equation (3) we have
y+1=8
y=8-1
y=7.
x= - 2,y=7.