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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?

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

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