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

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satellite73
 3 years ago
Best ResponseYou've already chosen the best response.1i mean square the matrix

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.1i got \[\left[ \begin{array}{ c c } x^2+3y & 3x+9 \\ xy+3y & 3y+9 \end{array} \right]\]

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.1assuming the matrix is \[\left[ \begin{array}{ c c } x & 3 \\ y & 3 \end{array} \right]\]

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.1that means \[3x+9=3\] so \[x=2\] and also \(y=2\)

monroe17
 3 years ago
Best ResponseYou've already chosen the best response.0once you square the matrix, how do you determine the x and y values though?

monroe17
 3 years ago
Best ResponseYou've already chosen the best response.0oh nevermind. how'd you get 3x+9=3

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.1you have \[\left[ \begin{array}{ c c } x^2+3y & 3x+9 \\ x^2+3y & 3y+9 \end{array} \right]=\left[ \begin{array}{ c c } x & 3 \\ y& 3 \end{array} \right]\]

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.1assuming my squaring is correct

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.1so that means each entry has to be the same for the matrices to be equal

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.1therefore \(3x+9=3\implies x=2\) 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

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.1sorry i meant \(3y+9=3\implies x=2\)

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.1you can check that this is right by squaring and seeing that you get the same matrix back

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.1also you might want to check that i squared the matrix correctly, but i think it is right

monroe17
 3 years ago
Best ResponseYou've already chosen the best response.0okay:) So, the steps to a problem like this is to first follow the formula (A^2=A) for the matrix. Then just solve..

monroe17
 3 years ago
Best ResponseYou've already chosen the best response.0when it said A^2=A I first thought it mean like x^2 and 3^2.. i haven't learned this yet lol
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