Finite Math Examples

$[\begin{array}{c} 45 & 27 \\ 100 & 104 \end{array}] + [\begin{array}{c} 74 & 57 \\ 112 & 123 \end{array}]$

Step 1

Add the corresponding elements.

$[\begin{array}{c} 45 + 74 & 27 + 57 \\ 100 + 112 & 104 + 123 \end{array}]$

Step 2

Simplify each element.

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Step 2.1

Add $45$ and $74$ .

$[\begin{array}{c} 119 & 27 + 57 \\ 100 + 112 & 104 + 123 \end{array}]$

Step 2.2

Add $27$ and $57$ .

$[\begin{array}{c} 119 & 84 \\ 100 + 112 & 104 + 123 \end{array}]$

Step 2.3

Add $100$ and $112$ .

$[\begin{array}{c} 119 & 84 \\ 212 & 104 + 123 \end{array}]$

Step 2.4

Add $104$ and $123$ .

$[\begin{array}{c} 119 & 84 \\ 212 & 227 \end{array}]$

Step 3

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$119 \cdot 227 - 212 \cdot 84$

Step 4

Simplify the determinant.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply $119$ by $227$ .

$27013 - 212 \cdot 84$

Step 4.1.2

Multiply $- 212$ by $84$ .

$27013 - 17808$

Step 4.2

Subtract $17808$ from $27013$ .

$9205$