Linear Algebra Examples

$x = y z$

Step 1

Rewrite the equation as $y z = x$ .

$y z = x$

Step 2

Divide each term in $y z = x$ by $z$ and simplify.

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Step 2.1

Divide each term in $y z = x$ by $z$ .

$\frac{y z}{z} = \frac{x}{z}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $z$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{y z}{z} = \frac{x}{z}$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{x}{z}$

Step 3

Set the denominator in $\frac{x}{z}$ equal to $0$ to find where the expression is undefined.

$z = 0$

Step 4

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$(- \infty, 0) \cup (0, \infty)$

Set-Builder Notation:

${x | x \neq 0}$