From the previous section, we saw that the process of calculating a determinate can be long and complex. Due to…

For square matrices, we can calculate a special value called the determinate. This value has a few uses, most notably,…

Suppose that we have a matrix A, and we wish to find a matrix I, with the property that AI…

Geometric transformations are an example of a mapping used to manipulate vectors in space. They are typically used to do…

With matrix multiplication, we can extend the ways that we manipulate matrices. One method of doing this is matrix mappings…

We discussed that scalar multiplication applies to matrices by multiplying the scalar by each component in the matrix. In order…

The transpose operation is one that allows us to swap the rows and columns of a matrix. For example, suppose…

Now that we have introduced how matrices are used in linear systems, we can look at the operations and properties…

We can extend the idea of row echelon format to make it easier to identify the solution to the system.…

Solving linear systems is a problem core to Linear Algebra. You will notice that so far we have already encountered…