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Matrices and Vectors

A collection of numbers (called entries) contained within a pair of [ ] brackets is called a matrix. A matrix is labeled by a variable, which is usually a capitalized letter. In a sense, matrices are like sets of data, except that a matrix is made up of rows and columns of data as opposed to just one row of data.

A vector is a matrix that only contains one row or one column. It can be thought of as a one-dimensional array of numbers, while a matrix is generally considered a multidimensional array of numbers.

A matrix is defined by the numbers of rows it contains and the number of columns it contains (in that order). There are a large number of types and uses for matrices, but you will only need to know how to perform:

addition
subtraction
scalar multiplication of matrices
multiplying a matrix by another matrix

How to Add Matrices

How to Subtract Matrices

How to Multiply Matrices

Multiplying a Matrix by Another Matrix

You can multiply a matrix by another matrix, but there are more steps involved than multiplying by the scalar. We can find the product of two matrices by finding the “dot products” of the corresponding rows and columns.

How to Find the Dot Product

To multiply matrices together, they do not have to have the same number of rows and columns, but the second matrix must have the same number of rows as the first has columns. This will create a matrix with the same number of rows as the first and the same number of columns as the second.