Question

find x and y I'm terms of matrix​

Answer 1

GIVEN :–

$\\ \sf \:x + 2y = \begin{bmatrix} 2&0&3 \\ \\ 1& - 1&1\end{bmatrix} \: \: and \: \:2x - y =\begin{bmatrix} 1& - 4& - 5 \\ \\ 0& \: 2& - 1\end{bmatrix}$

TO FIND :–

• x and y = ?

SOLUTION :–

• According to the question –

$\\ \sf \implies x + 2y = \begin{bmatrix} 2&0&3 \\ \\ 1& - 1&1\end{bmatrix} \: \: \: - - - eq.(1)$

• And –

$\\ \sf \implies 2x - y =\begin{bmatrix} 1& - 4& - 5 \\ \\ 0& \: 2& - 1\end{bmatrix} \: \: \:$

• Multiply with '2' –

$\\ \sf \implies 4x - 2y =\begin{bmatrix} 2& - 8& - 10 \\ \\ 0& \: 4& -2\end{bmatrix} \: \: \: - - - eq.(2)$

• Add eq.(1) and eq.(2) –

$\\ \sf \implies x + 2y + 4x - 2y = \begin{bmatrix} 2&0&3 \\ \\ 1& - 1&1\end{bmatrix} \: + \: \begin{bmatrix} 2& - 8& - 10 \\ \\ 0& \: 4& -2\end{bmatrix} \: \: \:$

$\\ \sf \implies 5x = \begin{bmatrix} 2 + 2&0 - 8&3 - 10 \\ \\ 1 + 0& - 1 + 4&1 - 2\end{bmatrix}$

$\\ \sf \implies 5x = \begin{bmatrix} 4& - 8& - 7 \\ \\ 1&3& - 1\end{bmatrix}$

$\\ \sf \implies x = \left (\dfrac{1}{5} \right) \begin{bmatrix} 4& - 8& - 7 \\ \\ 1&3& - 1\end{bmatrix}$

• Using eq.(1) –

$\\ \sf \implies \left (\dfrac{1}{5} \right) \begin{bmatrix} 4& - 8& - 7 \\ \\ 1&3& - 1\end{bmatrix} + 2y = \begin{bmatrix} 2&0&3 \\ \\ 1& - 1&1\end{bmatrix}$

$\\ \sf \implies \begin{bmatrix} \dfrac{4}{5} & - \dfrac{8}{5} & - \dfrac{7}{5} \\ \\ \dfrac{1}{5} & \dfrac{3}{5} & - \dfrac{1}{5} \end{bmatrix} + 2y = \begin{bmatrix} 2&0&3 \\ \\ 1& - 1&1\end{bmatrix}$

$\\ \sf \implies 2y = \begin{bmatrix} 2&0&3 \\ \\ 1& - 1&1\end{bmatrix} - \begin{bmatrix} \dfrac{4}{5} & - \dfrac{8}{5} & - \dfrac{7}{5} \\ \\ \dfrac{1}{5} & \dfrac{3}{5} & - \dfrac{1}{5} \end{bmatrix}$

$\\ \sf \implies 2y = \begin{bmatrix} \dfrac{6}{5} & \dfrac{8}{5} & \dfrac{22}{5} \\ \\ \dfrac{4}{5} & - \dfrac{8}{5} & \dfrac{6}{5} \end{bmatrix}$

$\\ \sf \implies 2y = 2 \begin{bmatrix} \dfrac{3}{5} & \dfrac{4}{5} & \dfrac{11}{5} \\ \\ \dfrac{2}{5} & - \dfrac{4}{5} & \dfrac{3}{5} \end{bmatrix}$

$\\ \sf \implies y = \begin{bmatrix} \dfrac{3}{5} & \dfrac{4}{5} & \dfrac{11}{5} \\ \\ \dfrac{2}{5} & - \dfrac{4}{5} & \dfrac{3}{5} \end{bmatrix}$