techtree / Linear algebra

Adding and scaling vectors

Add vectors entry by entry (tip to tail); scale by multiplying every entry.

38 seconds

[21]+[13]=[34]2[21]=[42]\begin{bmatrix} 2 \\ 1 \end{bmatrix} + \begin{bmatrix} 1 \\ 3 \end{bmatrix} = \begin{bmatrix} 3 \\ 4 \end{bmatrix} \qquad 2 \begin{bmatrix} 2 \\ 1 \end{bmatrix} = \begin{bmatrix} 4 \\ 2 \end{bmatrix}
Transcript

Here are two vectors. Two, one. And one, three.

To add them, add matching entries. Two plus one is three. One plus three is four.

As arrows, start the second one where the first one ends. The sum goes from the start to where you land.

Add them in the other order, and you land in the same place.

To scale a vector, multiply every entry by the same number. Two times two, one is four, two.

Same direction, twice as long. Times one half, it is half as long.

Times minus one, it turns around.

Adding is tip to tail. Scaling is stretching.

Needs

  • Vectors video
    A vector is a list of numbers, and also an arrow.

Leads to