Finite Math Examples

$[\begin{array}{c} 1 & 8 & 7 \\ 2 & 9 & 6 \\ 3 & 4 & 5 \end{array}] \cdot [\begin{array}{c} 1 & 6 \\ 3 & 4 \\ 5 & 2 \end{array}]$

Step 1

Multiply each row in the first matrix by each column in the second matrix.

$[\begin{array}{c} 1 \cdot 1 + 8 \cdot 3 + 7 \cdot 5 & 1 \cdot 6 + 8 \cdot 4 + 7 \cdot 2 \\ 2 \cdot 1 + 9 \cdot 3 + 6 \cdot 5 & 2 \cdot 6 + 9 \cdot 4 + 6 \cdot 2 \\ 3 \cdot 1 + 4 \cdot 3 + 5 \cdot 5 & 3 \cdot 6 + 4 \cdot 4 + 5 \cdot 2 \end{array}]$

Step 2

Simplify each element of the matrix by multiplying out all the expressions.

$[\begin{array}{c} 60 & 52 \\ 59 & 60 \\ 40 & 44 \end{array}]$