A **vector** has two pieces of infromation contained within it:

- the direction in which the vector points
- the
**magnitude**of the vector*(which is just the length of the vector)*

Vector expressions:

### Column Vectors

### Row Vectors

### Spaces

In fact, for any matrix, each column in the matrix is technically a **column vector**. For example, in matrix

there are five **column vectors**:

Because each of these column vectors has two components, it means they are vectors in two-dimensional space,

Similarly, we could also say that **row vectors**:

Whe we look at a set of row vectors or column vectors, it’s important to understand the space that the vectors occupy. There are two aspects we want to consider: first, the space

For instance, the given **two row vectors** above:

- because they each have
components, they are vectors in , and - because there are
vectors, they form a two dimensional plane in

### Vectors can be moved

To sketch a vector, we often start at the origin and move out to the “coordinate point” that’s expressed by the vector. Placing the starting point of the vector at the origin means that you’re sketching the vector in standard position.

For instance, the two-dimensional vectors:

could all be sketched together in

Each of these vectors has its **initial point** at the origin (each vector “starts” at **terminal point** at the location described by the vector.

The information contained in a vector is only its direction and its length, whic means vectors don’t always have to start at the origin.