Question

find matrices x and y if
2x +y = ( 4 4 7
7 3 4 )
and x-2y= (-3 2 1
1 -1 2)​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

$\begin{gathered}\rm :\longmapsto\:2x + y=\left[\begin{array}{ccc}4&4&7\\7&3&4\end{array}\right]\end{gathered} - - - (1)$

and

$\begin{gathered}\rm :\longmapsto\:x - 2y=\left[\begin{array}{ccc} - 3&2&1\\1& - 1&2\end{array}\right]\end{gathered} - - - (2)$

On multiply equation (1) by 2, we get

$\begin{gathered}\rm :\longmapsto\:4x + 2y=\left[\begin{array}{ccc}8&8&14\\14&6&8\end{array}\right]\end{gathered} - - - (3)$

On adding equation (3) and equation (2), we get

$\begin{gathered}\rm :\longmapsto\:5x =\left[\begin{array}{ccc}5&10&15\\15&5&10\end{array}\right]\end{gathered}$

$\begin{gathered}\bf :\longmapsto\:x =\left[\begin{array}{ccc}1&2&3\\3&1&2\end{array}\right]\end{gathered} - - - (4)$

Now,

Multiply equation (2) by 2, we get

$\begin{gathered}\rm :\longmapsto\:2x - 4y=\left[\begin{array}{ccc} - 6&4&2\\2& -2&4\end{array}\right]\end{gathered} - - - (5)$

On Subtracting equation (2) from equation (1), we get

$\begin{gathered}\rm :\longmapsto\:5y=\left[\begin{array}{ccc} 10&0&5\\5& 5&0\end{array}\right]\end{gathered} - - - (5)$

$\begin{gathered}\bf :\longmapsto\:y=\left[\begin{array}{ccc} 2&0&1\\1& 1&0\end{array}\right]\end{gathered} - - - (6)$

Answer 2

Answer:

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