turkey-yks 2012 Q36

turkey-yks · Other · lys1-math Matrices Linear System and Inverse Existence
For a matrix A with multiplicative inverse $A^{-1}$,
$$\left[ \begin{array} { l l } 2 & 1 \end{array} \right] \cdot \left[ \begin{array} { l l } 1 & 0 \\ 3 & 1 \end{array} \right] ^ { - 1 } \cdot \left[ \begin{array} { l } 1 \\ 4 \end{array} \right] = [ a ]$$
In the matrix equation, what is a?
A) 1
B) 2
C) 3
D) 4
E) 5
For a matrix A with multiplicative inverse $A^{-1}$,

$$\left[ \begin{array} { l l } 2 & 1 \end{array} \right] \cdot \left[ \begin{array} { l l } 1 & 0 \\ 3 & 1 \end{array} \right] ^ { - 1 } \cdot \left[ \begin{array} { l } 1 \\ 4 \end{array} \right] = [ a ]$$

In the matrix equation, what is a?

A) 1\\
B) 2\\
C) 3\\
D) 4\\
E) 5