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I have two boolean matrices:

A = |1 1 0|     |0 1 0|     |0 0 1|  and  B = |1 0 0|     |1 1 1|     |0 0 1| 

What is the result of A x B and what are the steps needed to attain the result?

Note: My textbook says that the answer to the above is:

A x B = |1 1 1|         |1 1 1|         |0 0 1| 

and that A * B is not equal to A x B. Unfortunately, it does not give the steps needed to find the solution.

  • 0
    It means "A dot B"2011-03-11

1 Answers 1

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I think it is the same as conventional matrix multiplication just that the multiplication is replaced by the "and" operation while the addition is replaced by the "or" operation.

Hence, $A \times B = \begin{bmatrix} 1 & 1 & 0 \\\ 0 & 1 & 0 \\\ 0 & 0 & 1 \end{bmatrix} \times \begin{bmatrix} 1 & 0 & 0 \\\ 1 & 1 & 1 \\\ 0 & 0 & 1 \end{bmatrix}$

$A \times B = \begin{bmatrix} (1 \& 1) || (1 \& 1) || (0 \& 0) & (1 \& 0) || (1 \& 1) || (0 \& 0) & (1 \& 0) || (1 \& 1) || (0 \& 1) \\\ (0 \& 1) || (1 \& 1) || (0 \& 0) & (0 \& 0) || (1 \& 1) || (0 \& 0) & (0 \& 0) || (1 \& 1) || (0 \& 1) \\\ (0 \& 1) || (0 \& 1) || (1 \& 0) & (0 \& 0) || (0 \& 1) || (1 \& 0) & (0 \& 0) || (0 \& 1) || (1 \& 1) \end{bmatrix}$

$A \times B = \begin{bmatrix} 1 & 1 & 1 \\\ 1 & 1 & 1 \\\ 0 & 0 & 1 \end{bmatrix}$

  • 0
    http://matrix.reshish.com/multCalculation.php2016-11-25