If [ lll 1 & 1 & 1 0 & 1 & 1 0 & 0 & 1 ] [ l x y z ]= [ l 6 3 2 ]… - Vidyadip

MCQ

If $\left[\begin{array}{lll}1 & 1 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 1\end{array}\right]\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}6 \\ 3 \\ 2\end{array}\right]$, then the value of $(2 x+y-z)$ is

A
$1$
B
$2$
C
$3$
✓
$5$

✓

Answer

Correct option: D.

$5$

$\left[\begin{array}{lll} 1 & 1 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{array}\right]\left[\begin{array}{l} x \\ y \\ z \end{array}\right]=\left[\begin{array}{l} 6 \\ 3 \\ 2 \end{array}\right] $
$\therefore x+y+z=6 ..... (i)$
$y+z=3 ........ (ii)$
$ z=2 ....... (iii)$
$\Rightarrow y+2=3$
$[$Using $(ii)$ and $(iii)]$
$\Rightarrow y=1$
$\Rightarrow x+1+2=6$
$\Rightarrow x=3$
$[$Using $(i), (iii)$ and $(iv)]$
So, $2 x+y-z=(2 \times 3)+1-2$
$=6+1-2=5$

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