Math, asked by AkashMathematics, 1 month ago

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} \  \textless \ br /\  \textgreater \ . Find X and Y ?​

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Answered by samirbhatkar283
1

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Answered by BrainlyBAKA
5

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}}

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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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