Find the Matrix X and Y

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

Adding 1 and 2

$x + y +x-y = left[ beginarray l l 5 & 2 \ 0 & 9 endarray right] + left[ beginarray l l 3 & 6 \ 0 & - 1 endarray right]$

$2 x = frac 1 2 left[ beginarray l l 8 & 8 \ 0 & 8 endarray right]$

$x = left[ beginarray l l 4 & 4 \ 0 & 4 endarray right]$

to Find Y

$left[ beginarray l l 1 & 4 \ 0 & 4 endarray right] + y = left[ beginarray l l 5 & 2 \ 0 & 9 endarray right]$

$y = left[ beginarray l l 5 & 2 \ 0 & 9 endarray right] - left[ beginarray l l 4 & 4 \ 0 & 4 endarray right]$

$y = left[ beginarray l l 1 & 2 \ 0 & 3 endarray right]$

so $x = left[ beginarray l l 4 & 4 \ 0 & 4 endarray right]$ and $y = left[ beginarray l l 1 & 2 \ 0 & 3 endarray right]$ is this correct or not ?

2 Answers
2

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

You have the right ideas but I see multiple mistakes.

$$X+Y+X-Y = left[ beginarray l l 5 & 2 \ 0 & 9 endarray right] + left[ beginarray l l 3 & 6 \ 0 & - 1 endarray right]$$

$$2 X = colorred1 cdot left[ beginarray l l 8 & 8 \ 0 & 8 endarray right]$$

$$X = left[ beginarray l l 4 & 4 \ 0 & 4 endarray right]$$

to Find $Y$

$$beginbmatrix colorred4 & 4 \ 0 & 4 endbmatrix + y = left[ beginarray l l 5 & 2 \ 0 & 9 endarray right]$$

$$Y = left[ beginarray l l 5 & 2 \ 0 & 9 endarray right] - left[ beginarray l l 4 & 4 \ 0 & 4 endarray right]$$

$$Y = left[ beginarray l l 1 & colorred-2 \ 0 & colorred5 endarray right]$$

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