Investigating Linear Algebra and Matrices Module Overview

Introduction

We will explore different ways to portray math that you may already know. In this Module, we will discover Matrices. Matrices can be used to display and organize data. When data is organized in a matrix, you can add, subtract and even multiply the data to manipulate it! You will come to see that matrices have many of the same properties as real numbers, except when multiplied! Not only can you display data with matrices, you can also solve systems of equations and transform geometric figures.

Essential Questions

How can we represent data in matrix form?
How do we add, subtract and multiply matrices?
What is an identity matrix and how does it behave?
How do we find the determinant and the inverse of a 2x2 matrix?
How do we solve systems of equations using inverse matrices?
How do we find the area of a parallelogram using matrices?
How do you work with matrices as transformations in the plane?

Matrices Key Terms

The following key terms will help you understand the content in this module.

Determinant - the product of the elements on the main diagonal minus the product of the elements of the other diagonal (for a 2 x 2 matrix)

Dimensions of a Matrix - the number of rows by the number of columns

Identity Matrix - a square matrix with 1's on the main diagonal and 0's everywhere else

Matrix - a rectangular arrangement of numbers into rows and columns

Scalar - in matrix algebra, a real number is called a scalar

Square Matrix - a matrix with the same number of rows and columns

Vector - a quantity that has both magnitude and direction

Zero Matrix - a matrix whose entries are all zeros

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