QS-015 · Linear Algebra · Easy
Finding x,y,z in a System of Linear Equations
What values of $x,y$ and $z$ satisfy the following system of linear equations?
$$ \begin{bmatrix} 1&2&3\\ 1&3&4\\ 2&2&3 \end{bmatrix} \begin{bmatrix} x\\ y\\ z \end{bmatrix} = \begin{bmatrix} 6\\ 8\\ 12 \end{bmatrix} $$
1. $x=6,\ y=3,\ z=2$
2. $x=12,\ y=3,\ z=-4$
3. $x=6,\ y=6,\ z=-4$
4. $x=12,\ y=-3,\ z=0$
What values of $x,y$ and $z$ satisfy the following system of linear equations?
$$ \begin{bmatrix} 1&2&3\\ 1&3&4\\ 2&2&3 \end{bmatrix} \begin{bmatrix} x\\ y\\ z \end{bmatrix} = \begin{bmatrix} 6\\ 8\\ 12 \end{bmatrix} $$
1. $x=6,\ y=3,\ z=2$
2. $x=12,\ y=3,\ z=-4$
3. $x=6,\ y=6,\ z=-4$
4. $x=12,\ y=-3,\ z=0$
Solution
The given system gives
$$ x+2y+3z=6 \rightarrow (1) $$ $$ x+3y+4z=8 \rightarrow (2) $$ $$ 2x+2y+3z=12 \rightarrow (3) $$
Apply $(3)-(1)$:
$$ x=6. $$
Substituting $x=6$ into equations $(1)$ and $(2)$:
$$ 2y+3z=0 $$ $$ 3y+4z=2 $$
Solving these equations gives
$$ y=6,\qquad z=-4. $$
Hence,
$$ x=6,\qquad y=6,\qquad z=-4. $$
Therefore, Option C is correct.
Open interactive problem view
Browse more quantitative interview problems