Linear Algebra Examples

$T n = 10 + (8 - 1) \cdot 4$

Step 1

Simplify.

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Step 1.1

Subtract $1$ from $8$ .

$T n = 10 + 7 \cdot 4$

Step 1.2

Multiply $7$ by $4$ .

$T n = 10 + 28$

Step 1.3

Add $10$ and $28$ .

$T n = 38$

Step 2

Divide each term in $T n = 38$ by $n$ and simplify.

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Step 2.1

Divide each term in $T n = 38$ by $n$ .

$\frac{T n}{n} = \frac{38}{n}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $n$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{T n}{n} = \frac{38}{n}$

Step 2.2.1.2

Divide $T$ by $1$ .

$T = \frac{38}{n}$

Step 3

Set the denominator in $\frac{38}{n}$ equal to $0$ to find where the expression is undefined.

$n = 0$

Step 4

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

Interval Notation:

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

Set-Builder Notation:

${n | n \neq 0}$

Step 5