Finite Math Examples

$[\begin{array}{c} 41 & 26 \\ 108 & 90 \end{array}] + [\begin{array}{c} 65 & 43 \\ 119 & 121 \end{array}]$

Step 1

Add the corresponding elements.

$[\begin{array}{c} 41 + 65 & 26 + 43 \\ 108 + 119 & 90 + 121 \end{array}]$

Step 2

Simplify each element.

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Step 2.1

Add $41$ and $65$ .

$[\begin{array}{c} 106 & 26 + 43 \\ 108 + 119 & 90 + 121 \end{array}]$

Step 2.2

Add $26$ and $43$ .

$[\begin{array}{c} 106 & 69 \\ 108 + 119 & 90 + 121 \end{array}]$

Step 2.3

Add $108$ and $119$ .

$[\begin{array}{c} 106 & 69 \\ 227 & 90 + 121 \end{array}]$

Step 2.4

Add $90$ and $121$ .

$[\begin{array}{c} 106 & 69 \\ 227 & 211 \end{array}]$

Step 3

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

$106 \cdot 211 - 227 \cdot 69$

Step 4

Simplify the determinant.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply $106$ by $211$ .

$22366 - 227 \cdot 69$

Step 4.1.2

Multiply $- 227$ by $69$ .

$22366 - 15663$

Step 4.2

Subtract $15663$ from $22366$ .

$6703$