Question

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

Answer 1

did you square it?

Answer 2

like 3^2?

Answer 3

i mean square the matrix

Answer 4

i got

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

Answer 5

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

Answer 6

that means
\[3x+9=3\] so \[x=-2\] and also \(y=-2\)

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

assuming my squaring is correct

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

ohhh okay!

Answer 15

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

Answer 16

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

Answer 17

gotta run

Answer 18

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

Answer 19

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