Find the Matrix X and Y

Question

$\text { Find the matrix } X \text { and } Y , \text { if } X + Y = \left[ \begin{array} { l l } { 5 } & { 2 } \\ { 0 } & { 9 } \end{array} \right] \text { and } X - Y = \left[ \begin{array} { c c } { 3 } & { 6 } \\ { 0 } & { - 1 } \end{array} \right]$

Adding 1 and 2

$x + y +x-y = \left[ \begin{array} { l l } { 5 } & { 2 } \\ { 0 } & { 9 } \end{array} \right] + \left[ \begin{array} { l l } { 3 } & { 6 } \\ { 0 } & { - 1 } \end{array} \right]$

$2 x = \frac { 1 } { 2 } \left[ \begin{array} { l l } { 8 } & { 8 } \\ { 0 } & { 8 } \end{array} \right]$

$x = \left[ \begin{array} { l l } { 4 } & { 4 } \\ { 0 } & { 4 } \end{array} \right]$

to Find Y

$\left[ \begin{array} { l l } { 1 } & { 4 } \\ { 0 } & { 4 } \end{array} \right] + y = \left[ \begin{array} { l l } { 5 } & { 2 } \\ { 0 } & { 9 } \end{array} \right]$

$y = \left[ \begin{array} { l l } { 5 } & { 2 } \\ { 0 } & { 9 } \end{array} \right] - \left[ \begin{array} { l l } { 4 } & { 4 } \\ { 0 } & { 4 } \end{array} \right]$

$y = \left[ \begin{array} { l l } { 1 } & { 2 } \\ { 0 } & { 3 } \end{array} \right]$

so $x = \left[ \begin{array} { l l } { 4 } & { 4 } \\ { 0 } & { 4 } \end{array} \right]$ and $y = \left[ \begin{array} { l l } { 1 } & { 2 } \\ { 0 } & { 3 } \end{array} \right]$ is this correct or not ?

Answer 1

You have several errors. The most critical one is while calculating $y$: $$y = \left[ \begin{array} { l l } { 5 } & { 2 } \\ { 0 } & { 9 } \end{array} \right] - \left[ \begin{array} { l l } { 4 } & { 4 } \\ { 0 } & { 4 } \end{array} \right] = \left[ \begin{array} { l l } { 1 } & { -2 } \\ { 0 } & { 5 } \end{array} \right]$$

Answer 2

You have the right ideas but I see multiple mistakes.

$$X+Y+X-Y = \left[ \begin{array} { l l } { 5 } & { 2 } \\ { 0 } & { 9 } \end{array} \right] + \left[ \begin{array} { l l } { 3 } & { 6 } \\ { 0 } & { - 1 } \end{array} \right]$$

$$2 X = \color{red}{1} \cdot \left[ \begin{array} { l l } { 8 } & { 8 } \\ { 0 } & { 8 } \end{array} \right]$$

$$X = \left[ \begin{array} { l l } { 4 } & { 4 } \\ { 0 } & { 4 } \end{array} \right]$$

to Find $Y$

$$\begin{bmatrix} {\color{red}{4}} & { 4 } \\ { 0 } & { 4 } \end{bmatrix} + y = \left[ \begin{array} { l l } { 5 } & { 2 } \\ { 0 } & { 9 } \end{array} \right]$$

$$Y = \left[ \begin{array} { l l } { 5 } & { 2 } \\ { 0 } & { 9 } \end{array} \right] - \left[ \begin{array} { l l } { 4 } & { 4 } \\ { 0 } & { 4 } \end{array} \right]$$

$$Y = \left[ \begin{array} { l l } { 1 } & { \color{red}-2 } \\ { 0 } & { \color{red}5 } \end{array} \right]$$