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

1 thought on “find matrices x and y if <br /> 2x +y = ( 4 4 7 <br /> 7 3 4 )<br /> and x-2y= (-3 2 1 <br />”

1. [tex]\large\underline{\sf{Solution-}}[/tex]

   Given that,

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

   and

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

   On multiply equation (1) by 2, we get

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

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

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

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

   Now,

   Multiply equation (2) by 2, we get

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

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

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

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

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