Question

If  \[\begin{bmatrix}a - b & 2a + c \\ 2a - b & 3c + d\end{bmatrix} = \begin{bmatrix}- 1 & 5 \\ 0 & 13\end{bmatrix}\] , find the value of b.

Answer 1

\[\begin{bmatrix}a - b & 2a + c \\ 2a - b & 3c + d\end{bmatrix} = \begin{bmatrix}- 1 & 5 \\ 0 & 13\end{bmatrix}\]

Corresponding elements of equal matrices are equal . 

\[ \Rightarrow a - b =\text{ - 1 and  } 2a - b = 0\]

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

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

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

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

Hence, the value of b is 2.