Linear Algebra Examples

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

Step 1

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

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

Step 2

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

$[\begin{array}{c} 62 \\ 18 \\ 96 \end{array}]$