Find the value of $a-2b$ if $\begin{bmatrix}a+4 & 3b\\8 & -6\end{bmatrix}=\begin{bmatrix}2a+2 & b+2\\8 & a-8b\end{bmatrix}\qquad$

Question

Note: This is a 3 part question, split as 3 separate questions here.

Answer 1

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.

Given: $\begin{bmatrix}a+4 & 3b\\8 & -6\end{bmatrix}=\begin{bmatrix}2a+2 & b+2\\8 & a-8b\end{bmatrix}\qquad$

By comparing the given two matrices of equal order, we can see that $a+4 = 2a+2, \:\:3b=b+2,\:\:-6=a-8b$

Solving first two equations,$\Rightarrow\:a=2,\:\:b=1$

which satisfy the equation $-6=a-8b$

$\therefore\:a-2b=2-2\times1=0$