SOLUTION: If A = [x, 3] [y, 2] determine the values of x and y for which A^2=A.

Algebra ->  Matrices-and-determiminant -> SOLUTION: If A = [x, 3] [y, 2] determine the values of x and y for which A^2=A.       Log On


   

Question 1159573: If A =
[x, 3]
[y, 2]
determine the values of x and y for which A^2=A.
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
+%28matrix%282%2C2%2Cx%2C3%2Cy%2C2%29%29++%28matrix%282%2C2%2Cx%2C3%2Cy%2C2%29%29+ = +%28matrix%282%2C2%2Cx%5E2%2B3y%2C3x%2B6%2Cxy%2B2y%2C3y%2B4%29%29+
From this, you can get four equations
1) +x%5E2%2B3y+=+x
2) +3x%2B6+=+3+
3) +xy%2B2y+=+y+
4) +3y%2B4+=+2+
(2) ==> x=-1
(4) ==> y=-2/3
You can verify (1) & (3) hold, as does
+%28matrix%282%2C2%2C-1%2C3%2C-2%2F3%2C2%29%29++%28matrix%282%2C2%2C-1%2C3%2C-2%2F3%2C2%29%29+ = +%28matrix%282%2C2%2C-1%2C3%2C-2%2F3%2C2%29%29+