Chapter 1:  Systems of Linear Equations

MA 237

Richard Hitt

Introduction

Mathematica has several built-in commands to help with linear algebra.  First we need to know how to input a matrix.  This is done by describing the matrix as a list of lists.

You can view the matrix in a rectangular array as follows.

Row vectors and column vectors can be entered as appropriate matrices.

Another way to describe a column vector is as the transpose of a row vector.  This might be easier to input.

Mathematica understands that v2 and v3 are the same.

Mathematica understands multiplication of a matrix by a vector using the following syntax.

Scalar multiplication can also be easily accomplished using the * or a blank space.  But be careful using the space because you can't always easily tell that its there.  So 3 c and 3c are interpreted differently in Mathematica -- the latter being the name of a new variable.

Test 1

For a few examples, here are some of the Test 1 problems worked out in Mathematica.

Problem 1

Problem 2

Problem 4