Question

Given X + Y = $\begin{gathered}\left[\begin{array}{ccc}1&2\\1&1\\\end{array}\right]\end{gathered}$and X - Y = $\begin{gathered}\left[\begin{array}{ccc}3&0\\-1&1\\\end{array}\right]\end{gathered}$ . Find X and Y ?​

Answer 1

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Answer 2

X + Y + X - Y = 2X

=> $\begin{gathered}\left[\begin{array}{ccc}1&2\\1&1\\\end{array}\right]\end{gathered}$ + $\begin{gathered}\left[\begin{array}{ccc}3&0\\-1&1\\\end{array}\right]\end{gathered}$ = 2X

=> $\begin{gathered}\left[\begin{array}{ccc}1+3&2+0\\1+(-1)&1+1\\\end{array}\right]\end{gathered}$ = 2X

=> $\begin{gathered}\left[\begin{array}{ccc}4&2\\0&2\\\end{array}\right]\end{gathered}$ = 2X

=> 2 $\begin{gathered}\left[\begin{array}{ccc}2&1\\0&1\\\end{array}\right]\end{gathered}$ = 2X

=> $\red{ X\:=}$$\red{\begin{gathered}\left[\begin{array}{ccc}2&1\\0&1\\\end{array}\right]\end{gathered}}$

X + Y = $\begin{gathered}\left[\begin{array}{ccc}1&2\\1&1\\\end{array}\right]\end{gathered}$

=> Y = $\begin{gathered}\left[\begin{array}{ccc}1&2\\1&1\\\end{array}\right]\end{gathered}$ - X

=> Y = $\begin{gathered}\left[\begin{array}{ccc}1&2\\1&1\\\end{array}\right]\end{gathered}$ - $\begin{gathered}\left[\begin{array}{ccc}2&1\\0&1\\\end{array}\right]\end{gathered}$

=> Y = $\begin{gathered}\left[\begin{array}{ccc}1-2&2-1\\1-0&1-1\\\end{array}\right]\end{gathered}$

=> $\red{ Y\:= }$ $\red{\begin{gathered}\left[\begin{array}{ccc}-1&1\\1&0\\\end{array}\right]\end{gathered}}$

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