# Finding missing matrix values

We have three matrices A; B; C that satisfy AB = C and such that

$$A = \begin{pmatrix} -1&2&-2&*\\ 2&-3&*&1\\ 0&-1&2&1 \end{pmatrix}$$

$$B = \begin{pmatrix} 2&3&*&4\\ -1&*&0&1\\ *&1&-2&0\\ 0&1&0&1 \end{pmatrix}$$ $$C = \begin{pmatrix} *&2&5&1\\ *&1&-2&-6\\ 3&1&-4&0 \end{pmatrix}$$

where a  indicates a missing values. Find the missing values and show the resulting matrices A; B; C.

After, multiplying A and B, I get the following matrix.

$$AB = \begin{pmatrix} -2&-2&-2*&0\\ 6&-3*&*&1\\ 0&-1&-4&1 \end{pmatrix}$$

Do I set AB equal to C and solve by getting it to reduced row echelon form? After that, assuming I get values for *, how do I know which * value goes to which matrix?

-
Label the stars $A_{1,4}$, $A_{2, 3}$, etc. This will let you know which stars go where. –  anorton Mar 3 '13 at 1:50
The multiplication result you have seems wrong to me. –  Jakob Weisblat Mar 3 '13 at 2:24
Why do you think that? –  Phil Kurtis Mar 3 '13 at 2:32
Why do you think he think that? –  leo Mar 3 '13 at 3:40
I'm not sure. A matrix m x n multiplied by a matrix n x p results a matrix m x p. –  Phil Kurtis Mar 3 '13 at 4:46

Just give labels to the unspecified entries, like $a,b,c,\ldots$. And it appears that your matrix multiplication is broken. See here for the correct result, for instance.