Question

find the matrix x if y =( 2 1 0 1) and 2 y^2 = 2 Y + x​

Answer 1

SOLUTION

GIVEN

$\displaystyle \sf{Y = \begin{pmatrix} 2 & 1\\ 0 & 1 \end{pmatrix} }$

$\displaystyle \sf{2 {Y}^{2} = 2Y + X}$

EVALUATION

Here it is given that

$\displaystyle \sf{Y = \begin{pmatrix} 2 & 1\\ 0 & 1 \end{pmatrix} }$

Now

$\displaystyle \sf{{Y}^{2} = \begin{pmatrix} 2 & 1\\ 0 & 1 \end{pmatrix} .\begin{pmatrix} 2 & 1\\ 0 & 1 \end{pmatrix} = \begin{pmatrix} 4 & 3\\ 0 & 1 \end{pmatrix} }$

Now

$\displaystyle \sf{2 {Y}^{2} = 2Y + X}$

$\displaystyle \sf{ \implies \: X = {Y}^{2} - 2Y }$

$\displaystyle \sf{ \implies \: X = 2\begin{pmatrix} 4 & 3\\ 0 & 1 \end{pmatrix} - 2. \begin{pmatrix} 2 & 1\\ 0 & 1 \end{pmatrix} }$

$\displaystyle \sf{ \implies \: X = \begin{pmatrix} 8 & 6\\ 0 & 2 \end{pmatrix} - \begin{pmatrix} 4 & 2\\ 0 & 2 \end{pmatrix} }$

$\displaystyle \sf{ \implies \: X = \begin{pmatrix} 4 & 4\\ 0 & 0 \end{pmatrix} }$

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