Simplify the Matrix [[3,2],[5,4]][[-2,3],[1,6]]

$[\begin{array}{c} 3 & 2 \\ 5 & 4 \end{array}] [\begin{array}{c} - 2 & 3 \\ 1 & 6 \end{array}]$

Step 1

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

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

Step 2

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

$[\begin{array}{c} - 4 & 21 \\ - 6 & 39 \end{array}]$