## anonymous 3 years ago If A= x 3 y 3 (matrix) determine the values of x and y for which A^2=A

1. anonymous

did you square it?

2. anonymous

like 3^2?

3. anonymous

i mean square the matrix

4. anonymous

i got $\left[ \begin{array}{ c c } x^2+3y & 3x+9 \\ xy+3y & 3y+9 \end{array} \right]$

5. anonymous

assuming the matrix is $\left[ \begin{array}{ c c } x & 3 \\ y & 3 \end{array} \right]$

6. anonymous

that means $3x+9=3$ so $x=-2$ and also $$y=-2$$

7. anonymous

once you square the matrix, how do you determine the x and y values though?

8. anonymous

oh nevermind. how'd you get 3x+9=3

9. anonymous

you have $\left[ \begin{array}{ c c } x^2+3y & 3x+9 \\ x^2+3y & 3y+9 \end{array} \right]=\left[ \begin{array}{ c c } x & 3 \\ y& 3 \end{array} \right]$

10. anonymous

assuming my squaring is correct

11. anonymous

so that means each entry has to be the same for the matrices to be equal

12. anonymous

therefore $$3x+9=3\implies x=-2$$ and $$3y+3=3\implies y=-2$$ and so the matrix must be $\left[ \begin{array}{ c c } -2 & 3 \\ -2 & 3 \end{array} \right]$ by substituting back

13. anonymous

sorry i meant $$3y+9=3\implies x=-2$$

14. anonymous

ohhh okay!

15. anonymous

you can check that this is right by squaring and seeing that you get the same matrix back

16. anonymous

also you might want to check that i squared the matrix correctly, but i think it is right

17. anonymous

gotta run

18. anonymous

okay:) So, the steps to a problem like this is to first follow the formula (A^2=A) for the matrix. Then just solve..

19. anonymous

when it said A^2=A I first thought it mean like x^2 and 3^2.. i haven't learned this yet lol