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# Find values of a and b if A=B,where A=$\begin{bmatrix}a + 4 & 3b\\8 & - 6\end{bmatrix},B=\begin{bmatrix}2a + 2 & b^2 + 2\\8 & b^2 - 5b\end{bmatrix}$

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.
Step1:
Given A=B.
Hence the given two matrices are equal .Hence their corresponding elements should be equal.
Let us compare the elements which can help to determine the value a
a+4=2a+2.
a-2a=2-4
-a=-2
a=2
Step2:
Now Let us compare the elements which can help to determine the value of b.
$3b=b^2+2$ or $b^2-5b=-6.$
Let us consider the first row
$3b=b^2+2$
$b^2-2b-b+2=0$
b(b-2)-1(b-2)=0
(b-1)(b-2)=0
b=1,2.------(1)
Let us consider the second row
$b^2-5b=-6$
$b^2-5b+6=0$
$b^3-3b-2b-6=0.$
b(b-3)-2(b-3)=0
(b-2)(b-3)=0
b=2,3-------(2)
since b=2 is common in both the equation (1) and (2)
$\Rightarrow a=2,b=2$.
answered Mar 21, 2013