Linear Algebra Examples

$[\begin{array}{c} 1 \\ - 7 \\ 1 \end{array}] \cdot [\begin{array}{c} 5 \\ 2 \\ 4 \end{array}]$

Step 1

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

$1 \cdot 5 - 7 \cdot 2 + 1 \cdot 4$

Step 2

Simplify.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $5$ by $1$ .

$5 - 7 \cdot 2 + 1 \cdot 4$

Step 2.1.2

Multiply $- 7$ by $2$ .

$5 - 14 + 1 \cdot 4$

Step 2.1.3

Multiply $4$ by $1$ .

$5 - 14 + 4$

Step 2.2

Subtract $14$ from $5$ .

$- 9 + 4$

Step 2.3

Add $- 9$ and $4$ .

$- 5$

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