In this course, we'll learn about three main topics: Linear Systems, Vector Spaces, and Linear Transformations. Along the way we'll learn about matrices and how to manipulate them.

1.1 What is a system of linear equations? Definition 1.1: A system of m linear equations in n unknown variables is a collection of m equations of the form a11x1 + a12x2 + a13x3 + a21x1 + a22x2 + a23x3 …

Abstract We define linear equations, both homogeneous and inhomogeneous, and describe what is certainly the oldest problem in linear algebra: finding the solutions of a system of linear equations.

In linear algebra, better theorems and more insight emerge if complex numbers are investigated along with real numbers. Thus we will begin by introducing the complex numbers and their basic properties.

Linear Algebra is strikingly similar to the algebra you learned in high school, except that in the place of ordinary single numbers, it deals with vectors.

This collection of exercises is designed to provide a framework for discussion in a junior level linear algebra class such as the one I have conducted fairly regularly at Portland State University.

Gilbert Strang, Introduction to Linear Algebra, 6th Edition (2023) 1. When can lines of lengths r,s,t form a triangle? They must satisfy the strict triangle inequalities r < s+t s < r +t t < r +s If we allow equality, …