Finite Math Examples

$[\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}] - [\begin{array}{c} 0.25 & 0.07 \\ 0.31 & 0.11 \end{array}]$

Step 1

Subtract the corresponding elements.

$[\begin{array}{c} 1 - 0.25 & 0 - 0.07 \\ 0 - 0.31 & 1 - 0.11 \end{array}]$

Step 2

Simplify each element.

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Step 2.1

Subtract $0.25$ from $1$ .

$[\begin{array}{c} 0.75 & 0 - 0.07 \\ 0 - 0.31 & 1 - 0.11 \end{array}]$

Step 2.2

Subtract $0.07$ from $0$ .

$[\begin{array}{c} 0.75 & - 0.07 \\ 0 - 0.31 & 1 - 0.11 \end{array}]$

Step 2.3

Subtract $0.31$ from $0$ .

$[\begin{array}{c} 0.75 & - 0.07 \\ - 0.31 & 1 - 0.11 \end{array}]$

Step 2.4

Subtract $0.11$ from $1$ .

$[\begin{array}{c} 0.75 & - 0.07 \\ - 0.31 & 0.89 \end{array}]$

Step 3

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

$0.75 \cdot 0.89 - (- 0.31 \cdot - 0.07)$

Step 4

Simplify the determinant.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply $0.75$ by $0.89$ .

$0.6675 - (- 0.31 \cdot - 0.07)$

Step 4.1.2

Multiply $- (- 0.31 \cdot - 0.07)$ .

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Step 4.1.2.1

Multiply $- 0.31$ by $- 0.07$ .

$0.6675 - 1 \cdot 0.0217$

Step 4.1.2.2

Multiply $- 1$ by $0.0217$ .

$0.6675 - 0.0217$

Step 4.2

Subtract $0.0217$ from $0.6675$ .

$0.6458$