# 1: What is Linear Algebra?

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Many difficult science problems can handled using the powerful, yet easy to use, mathematics of linear algebra. Unfortunately, because the subject (at least for those learning it) requires seemingly arcane and tedious computations involving large arrays of number known as matrices, the key concepts and the wide applicability of linear algebra are easily missed. Therefore, before we equip you with matrix skills, let us give some hints about what linear algebra is. The takeaway message is

﻿Linear algebra is the study of vectors and linear transformations.

﻿In broad terms, vectors are things you can add and linear transformations are very special functions of vectors that respect vector addition. To understand this a little better, lets try some examples. Please be prepared to change the way you think about some familiar mathematical objects and keep a pencil and piece of paper handy!

## Contributor

• David Cherney, Tom Denton, and Andrew Waldron (UC Davis)

• Thumbnail: In three-dimensional Euclidean space, these three planes represent solutions of linear equations, and their intersection represents the set of common solutions: in this case, a unique point. The blue line is the common solution to two of these equations. (CC BY-SA 3.0; Alksentrs via Wikipedia)

This page titled 1: What is Linear Algebra? is shared under a not declared license and was authored, remixed, and/or curated by David Cherney, Tom Denton, & Andrew Waldron.