Solve X', X for Y: Matrix Algebra Help

[pinto89a]

Find X if

X' * X =
(50, 300)
(300, 1000)

Then find Y if
Y * X =
(300, 2000)

Problem is that when I try to solve for X (or X') first, I get three equations with four unknowns (a11, a12, a21, a22). Any help?

 

[daveb]

I'm not sure what your notation is. Does X' mean adjoint, transpose, or what? You should have 4 equations in 4 unknowns, however, since each entry of the resultant matrix is found by multiplying elements of the individual matrices (and there are 4 elements in the resultant matrix).

 

[pinto89a]

Yes, the ' is transpose.

I get
a11 ^2 + a21 ^2 = 50
a11 * a12 + a21 * a22 = 300
a12 ^2 + a22 ^2 = 1000

but I can't get the fourth equation?

 

[TheoMcCloskey]

The matrix X must be 2 columns, but how many rows? Is X a simple 2x2 matrix?