Linear Algebra Examples

$A n B = c$

Step 1

Divide each term in $A n B = c$ by $n B$ and simplify.

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Step 1.1

Divide each term in $A n B = c$ by $n B$ .

$\frac{A n B}{n B} = \frac{c}{n B}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $n$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{A n B}{n B} = \frac{c}{n B}$

Step 1.2.1.2

Rewrite the expression.

$\frac{A B}{B} = \frac{c}{n B}$

Step 1.2.2

Cancel the common factor of $B$ .

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Step 1.2.2.1

Cancel the common factor.

$\frac{A B}{B} = \frac{c}{n B}$

Step 1.2.2.2

Divide $A$ by $1$ .

$A = \frac{c}{n B}$

Step 2

Set the denominator in $\frac{c}{n B}$ equal to $0$ to find where the expression is undefined.

$n B = 0$

Step 3

Divide each term in $n B = 0$ by $B$ and simplify.

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Step 3.1

Divide each term in $n B = 0$ by $B$ .

$\frac{n B}{B} = \frac{0}{B}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $B$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{n B}{B} = \frac{0}{B}$

Step 3.2.1.2

Divide $n$ by $1$ .

$n = \frac{0}{B}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $0$ by $B$ .

$n = 0$

Step 4

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

Interval Notation:

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

Set-Builder Notation:

${c | c \neq 0}$