Linear Algebra Examples

$[\begin{array}{c} 2 & y - 1 \\ x & z \end{array}]$

Step 1

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

$2 z - x (y - 1)$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$2 z - x y - x \cdot - 1$

Step 2.2

Multiply $- x \cdot - 1$ .

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Step 2.2.1

Multiply $- 1$ by $- 1$ .

$2 z - x y + 1 x$

Step 2.2.2

Multiply $x$ by $1$ .

$2 z - x y + x$