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# Find the value of a, b, c and d from the equation : $\begin{bmatrix} a-b & 2a+c \\ 2a-b & 3c+d \end{bmatrix} = \begin{bmatrix} -1 & 5 \\ 0 & 13 \end{bmatrix}$

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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
$\begin{bmatrix} a-b & 2a+c \\ 2a-b & 3c+d \end{bmatrix} = \begin{bmatrix} -1 & 5 \\ 0 & 13 \end{bmatrix}$
The given matrices are equal,hence their corresponding elements should be equal.
a-b=-1-------(1)
2a+c=5-------(2)
2a-b=0-------(3)
3c+d=13-----(4)
On solving equation (1) & (3),we get
On subtracting equation (3) from (1)
a-b=-1
2a-b=0
_________
-a=-1
a=1.
Step2:
Substitute the value of a in equation (1),we get
a-b=-1
1-b=-1
-b=-2
b=2.
Step3:
Consider the equation (2)
2a+c=5
Substitute the value of a in equation (2)
2(1)+c=5
2+c=5
c=3.
Step4:
Substitute the value of c in equation (4)
3c+d=13
3(3)+d=13
9+d=13
d=13-9
d=4.
a=1,b=2,c=3,d=4.
answered Apr 6, 2013