Algebra Examples

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

Step 1

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

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

Step 2

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

$[\begin{array}{c} 4 & - 1 & 2 & 2 \\ 1 & - 1 & 0 & 1 \\ 3 & 3 & 4 & - 1 \end{array}]$

Step 3

The matrix is in the most simplified form.

$[\begin{array}{c} 4 & - 1 & 2 & 2 \\ 1 & - 1 & 0 & 1 \\ 3 & 3 & 4 & - 1 \end{array}]$