# If $$\begin{bmatrix} xy & 4 \\ z+6 & x+y \end{bmatrix} = \begin{bmatrix} 8 & w \\ 0 & 6 \end{bmatrix}$$, then find values of x,y,z and w.

## 1 Answer

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
$\begin{bmatrix} xy & 4 \\ z+6 & x+y \end{bmatrix} = \begin{bmatrix} 8 & w \\ 0 & 6 \end{bmatrix}$
The above given matrices are equal hence their corresponding elements should be equal.
xy=8------(1)
4=w------(2)
z+6=0-----(3)
x+y=6-----(4)
Step2:
From equation (2) we have
w=4.
From equation (3) we have
z+6=0
z=-6.
From equation (1) we have
xy=8
x=$\frac{8}{y}$------(5)
Step3:
Substitute the value of x in equation (4)
x+y=6
$\frac{8}{y}+y=6$
$8+y^2=6y$
$y^2-6y+8=0$
$y^2-4y-2y+8=0$
y(y-4)-2(y-4)=0$\Rightarrow y=4,y=2$
Step4:
Substitute the value of y in equation (5)
$x=\frac{8}{y}$
$x=\frac{8}{4}$=2 or $x=\frac{8}{2}=4$
Hence w=4,z=-6,x=2 or 4,y=4 or 2.
answered Apr 5, 2013

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