Determine the resulting Boolean matrix of

Question

Determine the resulting Boolean matrix of

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I have a doubt when I'm going to multiply the resultant with the 2x2 matrix, it turns out that the resultant is 3x3, you can multiply matrices of different dimesion, can you explain me,

I made this:

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The picture in Spanish says in order:

Disjunction | Conjunction

Determine the resulting Boolean matrix.

This is supposed to multiply, but I see that they are matrices with different dimensions. As I do?

Answer 1

Looking at the first link, it seems that you need to calculate the Boolean Product. Calculating this is the same as calculating a regular product of two matrices except that the +'s denote disjunction (OR) and the $\cdot$'s denote conjunction (AND) like they normally do in Boolean algebra. Since you have the product of a $3 \times 2$ and a $2 \times 2$ matrix, the resulting matrix will be $3 \times 2$.

If $A$ is the first matrix, $B$ is the second, and $C$ is the Boolean Product of the two, then the element in row $i$ column $j$ of $C$ will be the Boolean dot product of row $i$ in $A$ with column $j$ in $B$.