iran-konkur 2018 Q140

iran-konkur · Other · konkur-riazi_1397_specialized Matrices Linear System and Inverse Existence
140-- Three pages with matrix equations. If $\begin{vmatrix} a & -1 & 3 \\ b & 2 & 4 \\ c & -2 & 1 \end{vmatrix} = 5$, then the three pages intersect. With which of the following lengths do they intersect?
$$\begin{bmatrix} 2 & -1 & 3 \\ 1 & 2 & 4 \\ 3 & -2 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} a \\ b \\ c \end{bmatrix}$$
(1) $-\dfrac{1}{3}$ (2) $-\dfrac{1}{2}$ (3) $\dfrac{1}{3}$ (4) $\dfrac{1}{2}$
\textbf{140--} Three pages with matrix equations. If $\begin{vmatrix} a & -1 & 3 \\ b & 2 & 4 \\ c & -2 & 1 \end{vmatrix} = 5$, then the three pages intersect. With which of the following lengths do they intersect?

$$\begin{bmatrix} 2 & -1 & 3 \\ 1 & 2 & 4 \\ 3 & -2 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} a \\ b \\ c \end{bmatrix}$$

(1) $-\dfrac{1}{3}$ \qquad (2) $-\dfrac{1}{2}$ \qquad (3) $\dfrac{1}{3}$ \qquad (4) $\dfrac{1}{2}$