Algebra Examples

$[\begin{array}{c} 7 & 0 & 1 \\ 0 & 3 & 1 \\ 0 & 2 & - 1 \end{array}] \cdot [\begin{array}{c} 0 & 2 & 1 \\ 0 & 3 & 0 \\ 2 & 0 & 2 \end{array}]$

Step 1

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

$[\begin{array}{c} 7 \cdot 0 + 0 \cdot 0 + 1 \cdot 2 & 7 \cdot 2 + 0 \cdot 3 + 1 \cdot 0 & 7 \cdot 1 + 0 \cdot 0 + 1 \cdot 2 \\ 0 \cdot 0 + 3 \cdot 0 + 1 \cdot 2 & 0 \cdot 2 + 3 \cdot 3 + 1 \cdot 0 & 0 \cdot 1 + 3 \cdot 0 + 1 \cdot 2 \\ 0 \cdot 0 + 2 \cdot 0 - 1 \cdot 2 & 0 \cdot 2 + 2 \cdot 3 - 0 & 0 \cdot 1 + 2 \cdot 0 - 1 \cdot 2 \end{array}]$

Step 2

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

$[\begin{array}{c} 2 & 14 & 9 \\ 2 & 9 & 2 \\ - 2 & 6 & - 2 \end{array}]$