Calculus Examples

$[\begin{array}{c} 5 & 3 \\ 3 & 2 \end{array}] x [\begin{array}{c} 4 \\ 0 \end{array}]$

Step 1

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

$[\begin{array}{c} 5 \cdot 4 + 3 \cdot 0 \\ 3 \cdot 4 + 2 \cdot 0 \end{array}] [\begin{array}{c} 5 & 3 \\ 3 & 2 \end{array}] x [\begin{array}{c} 4 \\ 0 \end{array}]$

Step 2

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

$[\begin{array}{c} 20 \\ 12 \end{array}] [\begin{array}{c} 5 & 3 \\ 3 & 2 \end{array}] x [\begin{array}{c} 4 \\ 0 \end{array}]$

Step 3

Matrices can only be multiplied if the number of columns in the first matrix is equal to the number of rows in the second matrix. The matrices cannot be multiplied.

$[\begin{array}{c} 20 \\ 12 \end{array}] [\begin{array}{c} 5 & 3 \\ 3 & 2 \end{array}] x [\begin{array}{c} 4 \\ 0 \end{array}] x [\begin{array}{c} 4 \\ 0 \end{array}]$