Linear Algebra Examples

$A (200) = - \frac{2000}{{(200)}^{2}}$

Step 1

Simplify.

Tap for more steps...

Step 1.1

Raise $200$ to the power of $2$ .

$A (200) = - \frac{2000}{40000}$

Step 1.2

Cancel the common factor of $2000$ and $40000$ .

Tap for more steps...

Step 1.2.1

Factor $2000$ out of $2000$ .

$A (200) = - \frac{2000 (1)}{40000}$

Step 1.2.2

Cancel the common factors.

Tap for more steps...

Step 1.2.2.1

Factor $2000$ out of $40000$ .

$A (200) = - \frac{2000 \cdot 1}{2000 \cdot 20}$

Step 1.2.2.2

Cancel the common factor.

$A (200) = - \frac{2000 \cdot 1}{2000 \cdot 20}$

Step 1.2.2.3

Rewrite the expression.

$A (200) = - \frac{1}{20}$

Step 2

Divide each term in $A (200) = - \frac{1}{20}$ by $200$ and simplify.

Tap for more steps...

Step 2.1

Divide each term in $A (200) = - \frac{1}{20}$ by $200$ .

$\frac{A (200)}{200} = \frac{- \frac{1}{20}}{200}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $200$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$\frac{A \cdot 200}{200} = \frac{- \frac{1}{20}}{200}$

Step 2.2.1.2

Divide $A$ by $1$ .

$A = \frac{- \frac{1}{20}}{200}$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$A = - \frac{1}{20} \cdot \frac{1}{200}$

Step 2.3.2

Multiply $- \frac{1}{20} \cdot \frac{1}{200}$ .

Tap for more steps...

Step 2.3.2.1

Multiply $\frac{1}{200}$ by $\frac{1}{20}$ .

$A = - \frac{1}{200 \cdot 20}$

Step 2.3.2.2

Multiply $200$ by $20$ .

$A = - \frac{1}{4000}$

Step 3

The domain is the set of all valid $A$ values.

${A | A = - \frac{1}{4000}}$

Step 4