iran-konkur 2014 Q140

iran-konkur · Other · konkur-riazi_1393 Simultaneous equations
140- Three planes are given by the following matrix equation: $$\begin{bmatrix} 2 & -1 & 1 \\ 1 & 3 & -1 \\ 1 & -11 & 5 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 6 \\ 4 \\ 2 \end{bmatrix}$$ What is the relationship of the two planes with respect to each other?
(1) Parallel (2) Coincident (3) Perpendicular (4) Lacking a common line of intersection
\textbf{140-} Three planes are given by the following matrix equation:
$$\begin{bmatrix} 2 & -1 & 1 \\ 1 & 3 & -1 \\ 1 & -11 & 5 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 6 \\ 4 \\ 2 \end{bmatrix}$$
What is the relationship of the two planes with respect to each other?

(1) Parallel \hfill (2) Coincident \hfill (3) Perpendicular \hfill (4) Lacking a common line of intersection

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