Linear Algebra Examples

$[\begin{array}{c} 2 \\ - 1 \\ 1 \end{array}] \cdot [\begin{array}{c} 5 \\ - 3 \\ 1 \end{array}]$

Step 1

The dot product of two vectors is the sum of the products of the their components.

$2 \cdot 5 - - 3 + 1 \cdot 1$

Step 2

Simplify.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $2$ by $5$ .

$10 - - 3 + 1 \cdot 1$

Step 2.1.2

Multiply $- 1$ by $- 3$ .

$10 + 3 + 1 \cdot 1$

Step 2.1.3

Multiply $1$ by $1$ .

$10 + 3 + 1$

Step 2.2

Add $10$ and $3$ .

$13 + 1$

Step 2.3

Add $13$ and $1$ .

$14$

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