Find the value of a and b, if $\begin{bmatrix} 2 & -2 \\ 3 & 7 \end{bmatrix} = \begin{bmatrix} 2 & a \\ 3 & 2a+b \end{bmatrix}$

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:
$\begin{bmatrix} 2 & -2 \\ 3 & 7 \end{bmatrix} = \begin{bmatrix} 2 & a \\ 3 & 2a+b \end{bmatrix}$
The given two matrices are equal,hence their corresponding elements should be equal.
-2=a.
7=2a+b----(1)
Hence a=-2.
Step2:
Substitute the value of a in equation (1)
2a+b=7.
2(-2)+b=7.
-4+b=7.
b=11.
a= -2,b=11.