## anonymous 5 years ago solve for x and y |x y| minus |-y x| |-y x| |x y | equals |4 6| |-4 6| This is a matrix problem and i dont understand it.

1. anonymous
2. anonymous

So im supposed to subtract the x's and y's?

3. anonymous

Generally, $\left[ \begin{array}{cc} a & b \\ c & d \end{array} \right] + \left[ \begin{array}{cc} e & f \\ g & h \end{array} \right] = \left[ \begin{array}{cc} a+e & b+f \\ c+g & d+h \end{array} \right]$ In this case, $\left[ \begin{array}{cc} x & y \\ -y & x \end{array} \right] - \left[ \begin{array}{cc} -y & x \\ x & y \end{array} \right] = \left[ \begin{array}{cc} x & y \\ -y & x \end{array} \right] + \left[ \begin{array}{cc} y & -x \\ -x & -y \end{array} \right]$ $= \left[ \begin{array}{cc} x+y & y-x \\ -y-x & x-y \end{array} \right] = \left[ \begin{array}{cc} 4 & 6 \\ -4 & 6 \end{array} \right]$ Now you effectively have 4 equations in two variables, so you should be able to either solve for each variable or show that no solutions satisfy all four equations.

4. anonymous

I solved this and got x=-1 and y=5. is that correct?

5. anonymous

... $\left[ \begin{array}{cc} x+y & y-x \\ -y-x & x-y \end{array} \right] = \left[ \begin{array}{cc} -1+5 & 5+1 \\ -5+1 & -1-5 \end{array} \right] = \left[ \begin{array}{cc} 4 & 6 \\ -4 & -6 \end{array} \right]$ no, that doesn't look right. $y-x=6 \rightarrow y=x+6; \ \ \ x-y=6 \rightarrow y=x-6; \ \ \ 6 \neq -6$ I don't think there is a solution.

6. anonymous

I cant see the third matrix

7. anonymous

where the 4s are