Linear Algebra Examples

$c {(A)}^{t} = (\frac{1}{C}) a^{t}$

Step 1

Combine $\frac{1}{C}$ and $a^{t}$ .

$c A^{t} = \frac{a^{t}}{C}$

Step 2

Divide each term in $c A^{t} = \frac{a^{t}}{C}$ by $A^{t}$ and simplify.

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Step 2.1

Divide each term in $c A^{t} = \frac{a^{t}}{C}$ by $A^{t}$ .

$\frac{c A^{t}}{A^{t}} = \frac{\frac{a^{t}}{C}}{A^{t}}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $A^{t}$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{c A^{t}}{A^{t}} = \frac{\frac{a^{t}}{C}}{A^{t}}$

Step 2.2.1.2

Divide $c$ by $1$ .

$c = \frac{\frac{a^{t}}{C}}{A^{t}}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$c = \frac{a^{t}}{C} \cdot \frac{1}{A^{t}}$

Step 2.3.2

Combine.

$c = \frac{a^{t} \cdot 1}{C A^{t}}$

Step 2.3.3

Multiply $a^{t}$ by $1$ .

$c = \frac{a^{t}}{C A^{t}}$

Step 3

Set the denominator in $\frac{a^{t}}{C A^{t}}$ equal to $0$ to find where the expression is undefined.

$C A^{t} = 0$

Step 4

Divide each term in $C A^{t} = 0$ by $A^{t}$ and simplify.

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Step 4.1

Divide each term in $C A^{t} = 0$ by $A^{t}$ .

$\frac{C A^{t}}{A^{t}} = \frac{0}{A^{t}}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $A^{t}$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{C A^{t}}{A^{t}} = \frac{0}{A^{t}}$

Step 4.2.1.2

Divide $C$ by $1$ .

$C = \frac{0}{A^{t}}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $0$ by $A^{t}$ .

$C = 0$

Step 5

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

Interval Notation:

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

Set-Builder Notation:

${a | a \neq 0}$