Question

If \[\begin{bmatrix}a + 4 & 3b \\ 8 & - 6\end{bmatrix} = \begin{bmatrix}2a + 2 & b + 2 \\ 8 & a - 8b\end{bmatrix}\] , write the value of a − 2b.

 

Answer 1

\[\begin{bmatrix}a + 4 & 3b \\ 8 & - 6\end{bmatrix} = \begin{bmatrix}2a + 2 & b + 2 \\ 8 & a - 8b\end{bmatrix}\]

Corresponding elements of equal matrices are equal .

\[ \therefore a + 4 =\text{2a + 2 and  } 3b = b + 2\]

\[ \Rightarrow 4 - 2 = \text{2a - a and } 3b - b = 2\]

\[ \Rightarrow a = \text{2 and } 2b = 2\]

\[ \Rightarrow a = \text{2 and } b = 1\]

\[ \therefore a - 2b = 2 - 2 = 0\]