# Interactive Online Modules for Matrix Algebra and Linear Algebra

## Vector Spaces

#### Vector Spaces Module (WebMathematica)

#### Sample Investigations:

##### Vector Space Activities:

#### Other Topics that Can Be Covered Using this Module:

- Linear Combination
- Linear Independence
- Span
- Spanning Set
- Basis
- Coordinates
- Vectors

#### Module Description

This module was developed using Mathematica, and it provides graphs of vector spaces in R^{3}.

The module shows vectors and vector operations from a geometric perspective. It is divided into three sections, each providing different tools.

Under the section **"For Collection of Linear Combinations,"** values of *a*, *b* and *c* are entered.
The module uses the values of *a*, *b* and *c* to produce the geometric representation (as dots) of the collection of all
linear combinations of the vectors, *nk+ml+si+sj* where *k*, *l*, *i*, and *j* are the vectors and the values of *n* range
from *–a* to *a*; the values of *m* range from *–b* to *b*
and the values of *s* range from *–c* to *c*.

**"Vectors"**section, vectors are associated with the names

*k*,

*l*,

*i*,

*j*. Any vector can be entered including the stored vectors labeled

*a0-a14*. Each vector is represented by a tick line segment with a color code. The module runs by Mathematica software. In Mathematica, vectors are entered using curly set notation. For instance, Mathematica recognizes {1, 2, 3} as a vector.

Under the **"Construction of Single Linear Combination"** section, you can assign values for the symbols *d* and *e*.
These values produce thin lines which are parallel copies (with the same colors as the vectors represented)
of scalar multiples of the vectors *k*, *l*. For instance, when the values d=2 and e=3 are entered,
the program produces thin lines with the same color as the vectors *k* and *l* respectively,
providing the length of the lines as twice the first vector *k* and three times the second vector *l*.
This section also has an option to enter a *w* vector, which can be used to produce the picture of the vector coming
from a linear combination of any vectors as well as *k* and *l* vectors.

**Figures can be rotated by moving mouse, and they can be resized by using mouse and "Shift" button on your keyboard.**