## monroe17 2 years ago If A= x 3 y 3 (matrix) determine the values of x and y for which A^2=A

1. satellite73

did you square it?

2. monroe17

like 3^2?

3. satellite73

i mean square the matrix

4. satellite73

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

5. satellite73

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

6. satellite73

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

7. monroe17

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

8. monroe17

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

9. satellite73

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. satellite73

assuming my squaring is correct

11. satellite73

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

12. satellite73

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. satellite73

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

14. monroe17

ohhh okay!

15. satellite73

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

16. satellite73

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

17. satellite73

gotta run

18. monroe17

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. monroe17

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