# Determinates in Terms of Cofactors

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

# Identity and Inverse Matrices

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

# Geometric Transformations

Geometric transformations are an example of a mapping used to manipulate vectors in space. They are typically used to do things like rotate, scale, and…

# Matrix and Linear Mapings

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

# Matrix Multiplication

We discussed that scalar multiplication applies to matrices by multiplying the scalar by each component in the matrix. In order to compute transformations, we also…

# Matrix Transposes

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

# Matrix Operations

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

# Reduced Row Echelon Form and Rank

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

# Matrix Representations of Systems

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

# Cross Products

The cross product is an operation that finds a third vector, , that is orthogonal to two vectors, and . The problem of finding a…