Question

The solution of the equation $\left[\begin{array}{ccc}1& 0& 1\\ -1& 1& 0\\ 0& -1& 1\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{c}1\\ 1\\ 2\end{array}\right]$ is $(x,y,z)=$

• A. $(1,1,1)$
• B. $(0,-1,2)$
• C. $(-1,2,2)$
• D. $(-1,0,2)$

Answer 1

Answer: (D)

$(-1,0,2)$

$\left[\begin{array}{ccc}1& 0& 1\\ -1& 1& 0\\ 0& -1& 1\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{c}1\\ 1\\ 2\end{array}\right]$
$\Rightarrow \left[\begin{array}{c}x+0y+z\\ -x+y+0z\\ 0x-y+z\end{array}\right]=\left[\begin{array}{c}1\\ 1\\ 2\end{array}\right]$
$\Rightarrow x+z=1,$
$-x+y=1$
and $-y+z=2$
On solving these equations, we get
$x=-1,y=0,z=2$