Linear Algebra Examples

$w = p (v (1 - v \cdot 2))$

Step 1

Simplify $p v (1 - v \cdot 2)$ .

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Step 1.1

Multiply $2$ by $- 1$ .

$w = p v (1 - 2 v)$

Step 1.2

Apply the distributive property.

$w = p v \cdot 1 + p v (- 2 v)$

Step 1.3

Simplify the expression.

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Step 1.3.1

Multiply $p$ by $1$ .

$w = p v + p v (- 2 v)$

Step 1.3.2

Rewrite using the commutative property of multiplication.

$w = p v - 2 p v \cdot v$

Step 1.4

Multiply $v$ by $v$ by adding the exponents.

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Step 1.4.1

Move $v$ .

$w = p v - 2 p (v \cdot v)$

Step 1.4.2

Multiply $v$ by $v$ .

$w = p v - 2 p v^{2}$

Step 2

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$