Basic linear algebra help! Find the LU-factorization of the matrix A = [a b, c d]

drestupinblac
Q: Find the LY-factorization of the matrix
$A = \begin{bmatrix} a & b \\ c & d \\ \end{bmatrix}$ that has 1's along the main diagonal of L. Are there any restrictions on the matrix A?

$L = \begin{bmatrix} 1 & 0 \\ e & 1 \\ \end{bmatrix} U = \begin{bmatrix} a & b \\ 0 & -eb + d \\ \end{bmatrix}$

restriction: ae (where e is some real number) must equal c.
...

I am just starting out in linear algebra and am probably completely off but I can't think
of another way to approach this question. Please help or tell me if I'm on the right tack.

Thanks!

drestupinblac

Oops, instead of "LY" I meant to put "LU"

anyone? or if the question doesn't make sense, can you please tell me so I can re-phrase?

TheoMcCloskey

I would replace "e" for what it needs to be, ie, "c/a".

Once done, you can now state a needed condition of matrix "A", specifically a condition of its element "a" for this solution to be valid.

Also, if you multiply L and U together again, you need to have the product yield the original matrix A again. Show this multiplication. Thus, take a look at the 2,2 element of U. You probrably don't want that to be zero or else the product will not be consistant with A. Rearranging element U(2,2) <> 0 will yield a familiar requirement.