taiwan-gsat 2025 Q2

taiwan-gsat · Other · gsat__math-b 5 marks Matrices Linear System and Inverse Existence
Let $A$ be a $3 \times 2$ matrix such that $A \left[ \begin{array} { c c } 1 & 0 \\ - 1 & 1 \end{array} \right] = \left[ \begin{array} { c c } 4 & - 6 \\ - 2 & 1 \\ 3 & 5 \end{array} \right]$ . If $A \left[ \begin{array} { l } 1 \\ 0 \end{array} \right] = \left[ \begin{array} { l } a \\ b \\ c \end{array} \right]$ , what is the value of $a + b + c$?
(1) 0
(2) 2
(3) 4
(4) 5
(5) 8
Let $A$ be a $3 \times 2$ matrix such that $A \left[ \begin{array} { c c } 1 & 0 \\ - 1 & 1 \end{array} \right] = \left[ \begin{array} { c c } 4 & - 6 \\ - 2 & 1 \\ 3 & 5 \end{array} \right]$ . If $A \left[ \begin{array} { l } 1 \\ 0 \end{array} \right] = \left[ \begin{array} { l } a \\ b \\ c \end{array} \right]$ , what is the value of $a + b + c$?\\
(1) 0\\
(2) 2\\
(3) 4\\
(4) 5\\
(5) 8