Algebra Examples

$[\begin{array}{c} 3 & 2 & - 4 \\ 5 & - 5 & - 3 \\ 4 & 1 & 1 \end{array}] [\begin{array}{c} 2 & - 4 & 1 \\ 5 & - 3 & 2 \\ 4 & 4 & - 5 \end{array}]$

Step 1

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

$[\begin{array}{c} 3 \cdot 2 + 2 \cdot 5 - 4 \cdot 4 & 3 \cdot - 4 + 2 \cdot - 3 - 4 \cdot 4 & 3 \cdot 1 + 2 \cdot 2 - 4 \cdot - 5 \\ 5 \cdot 2 - 5 \cdot 5 - 3 \cdot 4 & 5 \cdot - 4 - 5 \cdot - 3 - 3 \cdot 4 & 5 \cdot 1 - 5 \cdot 2 - 3 \cdot - 5 \\ 4 \cdot 2 + 1 \cdot 5 + 1 \cdot 4 & 4 \cdot - 4 + 1 \cdot - 3 + 1 \cdot 4 & 4 \cdot 1 + 1 \cdot 2 + 1 \cdot - 5 \end{array}]$

Step 2

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

$[\begin{array}{c} 0 & - 34 & 27 \\ - 27 & - 17 & 10 \\ 17 & - 15 & 1 \end{array}]$

Step 3

The matrix is in the most simplified form.

$[\begin{array}{c} 0 & - 34 & 27 \\ - 27 & - 17 & 10 \\ 17 & - 15 & 1 \end{array}]$