U7 Matrices(KA/PRE/U7)

Unit 7: Matrices

Introduction to Matrices

A matrix is a rectangular array of numbers organized in rows and columns.

Using Matrices to Represent Data

Matrices can store and manipulate data, such as images, graphs, or systems of equations.

Multiplying Matrices by Scalars

Each element of the matrix is multiplied by the scalar value.

Adding and Subtracting Matrices

Add/subtract corresponding elements of two matrices of the same dimensions.

Using Matrices to Transform the Plane

2x2 matrices can scale, rotate, shear, and reflect shapes on the plane.

Transforming 3D and 4D Vectors with Matrices

Higher-dimensional matrices can transform 3D/4D vectors (used in computer graphics, physics, etc).

Multiplying Matrices by Matrices

Matrix multiplication combines transformations or systems.

Representing Systems of Equations with Matrices

Systems of linear equations can be written as AX = B, solved using inverses or elimination.

Introduction to Matrix Inverses

The inverse of matrix A, written A⁻¹, satisfies A·A⁻¹ = I.

Solving Linear Systems with Matrices

Using the equation X = A⁻¹B if the inverse exists.

Quiz: Test Your Understanding

What is the identity matrix for 2x2 matrices?

1. [[0, 1], [1, 0]]
2. [[1, 0], [0, 1]]
3. [[1, 1], [1, 1]]