If A , = , [ * 20 c 1&2&x 3& - 1 &2 ] and B , = , [ * 20 c y x 1 … - Vidyadip

MCQ

If $A\, = \,\left[ {\begin{array}{*{20}{c}}
1&2&x\\
3&{ - 1}&2
\end{array}} \right]$ and $B\, = \,\left[ {\begin{array}{*{20}{c}}
y\\
x\\
1
\end{array}} \right]$ be such that $AB\, = \,\left[ {\begin{array}{*{20}{c}}
6\\
8
\end{array}} \right],$ then

✓
$y = 2x$
B
$y = -2x$
C
$y = x$
D
$y = -x$

✓

Answer

Correct option: A.

$y = 2x$

a
Let $A = \left[ {\begin{array}{*{20}{c}}
1&2&x\\
3&{ - 1}&2
\end{array}} \right]$ and $B = \left[ {\begin{array}{*{20}{c}}
y\\
x\\
1
\end{array}} \right]$

$AB = \left[ {\begin{array}{*{20}{c}}
1&2&x\\
3&{ - 1}&2
\end{array}} \right]\left[ {\begin{array}{*{20}{c}}
y\\
x\\
1
\end{array}} \right]$

$ \Rightarrow \left[ {\begin{array}{*{20}{c}}
6\\
8
\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}
{y + 2x + x}\\
{3y - x + 2}
\end{array}} \right]$

$ \Rightarrow \left[ {\begin{array}{*{20}{c}}
6\\
8
\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}
{y + 3x}\\
{3y - x + 2}
\end{array}} \right]$

$ \Rightarrow y + 3x = 6$ and $3y - x = 6$

On solving, we gat

$x = \frac{6}{5}$ and $y = \frac{{12}}{5}$

$ \Rightarrow y = 2x$

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