turkey-yks 2015 Q36

turkey-yks · Other · lys1-math Matrices Linear System and Inverse Existence
Let $A$ and $B$ be $2 \times 1$ matrices and $t$ be a variable such that for all $x$ and $y$ values satisfying
$$x - y = 3$$
we have
$$\left[ \begin{array} { l } x \\ y \end{array} \right] = t A + B$$
Accordingly, which of the following could matrices A and B be, respectively?
A) $\left[ \begin{array} { l } 1 \\ 0 \end{array} \right] , \left[ \begin{array} { l } 3 \\ 0 \end{array} \right]$
B) $\left[ \begin{array} { l } 0 \\ 1 \end{array} \right] , \left[ \begin{array} { l } 3 \\ 0 \end{array} \right]$
C) $\left[ \begin{array} { l } 1 \\ 1 \end{array} \right] , \left[ \begin{array} { l } 3 \\ 1 \end{array} \right]$
D) $\left[ \begin{array} { l } 1 \\ 1 \end{array} \right] , \left[ \begin{array} { l } 3 \\ 0 \end{array} \right]$
E) $\left[ \begin{array} { l } 1 \\ 1 \end{array} \right] , \left[ \begin{array} { r } 3 \\ - 3 \end{array} \right]$
Let $A$ and $B$ be $2 \times 1$ matrices and $t$ be a variable such that for all $x$ and $y$ values satisfying

$$x - y = 3$$

we have

$$\left[ \begin{array} { l } 
x \\
y
\end{array} \right] = t A + B$$

Accordingly, which of the following could matrices A and B be, respectively?\\
A) $\left[ \begin{array} { l } 1 \\ 0 \end{array} \right] , \left[ \begin{array} { l } 3 \\ 0 \end{array} \right]$\\
B) $\left[ \begin{array} { l } 0 \\ 1 \end{array} \right] , \left[ \begin{array} { l } 3 \\ 0 \end{array} \right]$\\
C) $\left[ \begin{array} { l } 1 \\ 1 \end{array} \right] , \left[ \begin{array} { l } 3 \\ 1 \end{array} \right]$\\
D) $\left[ \begin{array} { l } 1 \\ 1 \end{array} \right] , \left[ \begin{array} { l } 3 \\ 0 \end{array} \right]$\\
E) $\left[ \begin{array} { l } 1 \\ 1 \end{array} \right] , \left[ \begin{array} { r } 3 \\ - 3 \end{array} \right]$