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?

  • 2
    $\begingroup$ 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
  • 4
    $\begingroup$ 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
  • 1
    $\begingroup$ 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

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.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.