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

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satellite73Best ResponseYou've already chosen the best response.1
did you square it?
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
i mean square the matrix
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
i got \[\left[ \begin{array}{ c c } x^2+3y & 3x+9 \\ xy+3y & 3y+9 \end{array} \right]\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
assuming the matrix is \[\left[ \begin{array}{ c c } x & 3 \\ y & 3 \end{array} \right]\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
that means \[3x+9=3\] so \[x=2\] and also \(y=2\)
 one year ago

monroe17Best ResponseYou've already chosen the best response.0
once you square the matrix, how do you determine the x and y values though?
 one year ago

monroe17Best ResponseYou've already chosen the best response.0
oh nevermind. how'd you get 3x+9=3
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
you have \[\left[ \begin{array}{ c c } x^2+3y & 3x+9 \\ x^2+3y & 3y+9 \end{array} \right]=\left[ \begin{array}{ c c } x & 3 \\ y& 3 \end{array} \right]\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
assuming my squaring is correct
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
so that means each entry has to be the same for the matrices to be equal
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
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
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
sorry i meant \(3y+9=3\implies x=2\)
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
you can check that this is right by squaring and seeing that you get the same matrix back
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
also you might want to check that i squared the matrix correctly, but i think it is right
 one year ago

monroe17Best ResponseYou've already chosen the best response.0
okay:) So, the steps to a problem like this is to first follow the formula (A^2=A) for the matrix. Then just solve..
 one year ago

monroe17Best ResponseYou've already chosen the best response.0
when it said A^2=A I first thought it mean like x^2 and 3^2.. i haven't learned this yet lol
 one year ago
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