Algebra Examples

$[\begin{array}{c} x & 1 \\ x & 1 + x \end{array}]$

Step 1

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

$x (1 + x) - x \cdot 1$

Step 2

Simplify the determinant.

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$x \cdot 1 + x \cdot x - x \cdot 1$

Step 2.1.2

Multiply $x$ by $1$ .

$x + x \cdot x - x \cdot 1$

Step 2.1.3

Multiply $x$ by $x$ .

$x + x^{2} - x \cdot 1$

Step 2.1.4

Multiply $- 1$ by $1$ .

$x + x^{2} - x$

Step 2.2

Combine the opposite terms in $x + x^{2} - x$ .

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Step 2.2.1

Subtract $x$ from $x$ .

$x^{2} + 0$

Step 2.2.2

Add $x^{2}$ and $0$ .

$x^{2}$