Finite Math Examples

$[\begin{array}{c} \frac{2}{5} & \frac{3}{5} \end{array}] [\begin{array}{c} 0.9 & 0.1 \\ 0.2 & 0.8 \end{array}]$

Step 1

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

$[\begin{array}{c} \frac{2}{5} \cdot 0.9 + \frac{3}{5} \cdot 0.2 & \frac{2}{5} \cdot 0.1 + \frac{3}{5} \cdot 0.8 \end{array}]$

Step 2

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

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Rewrite $13$ as $1 (13)$ .

$[\begin{array}{c} \frac{12}{25} & \frac{1 (13)}{25} \end{array}]$

Cancel the common factors.

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Rewrite $25$ as $1 (25)$ .

$[\begin{array}{c} \frac{12}{25} & \frac{1 \cdot 13}{1 \cdot 25} \end{array}]$

Cancel the common factor.

$[\begin{array}{c} \frac{12}{25} & \frac{1 \cdot 13}{1 \cdot 25} \end{array}]$

Rewrite the expression.

$[\begin{array}{c} \frac{12}{25} & \frac{13}{25} \end{array}]$