About Us

Why Choose StudyPug

How it works

Pricing

Testimonials

Contact Us

Blog

Basic Math

Algebra

Geometry

Trigonometry

Calculus

Linear Algebra

Differential Equations

Statistics

Chemistry

Organic Chemistry

Physics

Microeconomics

For Students

For Parents

For Home Schoolers

For Teachers

Australia

Canada

Ireland

New Zealand

Singapore

United Kingdom

United States

Sitemap

Terms of Service

Privacy Policy

Matrix Addition Properties: Commutative and Associative Rules

Linear Algebra: Master Core Concepts & Applications

Linear Equations with Matrices

auto-gen

Row reduction and echelon forms

Linear combination and vector equations in \(R^n\)

Matrix equation Ax=b

Solution sets of linear systems

Application of linear systems

Solving systems of linear equations by graphing

Notation of matrices

The three types of matrix row operations

Representing linear system as a matrix

Representing a linear system as a matrix

Solving a linear system with matrices using Gaussian elimination

Linear Transformation

Linear independence

Image and range of linear transformations

Properties of linear transformation

The matrix of a linear transformation

Matrix Operations

Adding and subtracting matrices

Multiplying a matrix by a scalar

Multiplying a matrix by another matrix

Matrix multiplication

Zero matrix

Identity matrix

Properties of matrix addition

Properties of matrix scalar multiplication

Properties of matrix to matrix multiplication

Properties of matrix multiplication

Inverse of Matrices

The invertible matrix theorem

The inverse of a 2 x 2 matrix

The inverse of a 3 x 3 matrices with matrix row operations

2 x 2 invertible matrix

Solving linear systems using 2 x 2 inverse matrices

Subspace of \(\Bbb{R}^n\)

Properties of subspace

Column space

Null space

Dimension and rank

Determinant of a Matrix

Properties of determinants

The determinant of a 2 x 2 matrix

The determinant of a 3 x 3 matrix (General & Shortcut Method)

Solving linear systems using Cramer's Rule

Solving linear systems using Cramer"s Rule

Cramer"s Rule with 2 x 2 matrices

Eigenvalue and Eigenvectors

Eigenvalues and eigenvectors

The characteristic equation

Diagonalization

Complex eigenvalues

Discrete dynamical systems

Orthogonality and Least Squares

Inner product, length, and orthogonality

Orthogonal sets

Orthogonal projections

Least-squares problem

Applications to linear models

math

https://dmn92m25mtw4z.cloudfront.net/img/textbook/textbook-linear-algebra.png

Intro

Ex.1

Ex.2

Ex.3

Ex.4

In this section, we will look at the properties of matrix addition. These properties include the dimension property for addition, commutative property, and associative property. Note that for the dimension property, we are allowed to add or subtract two matrices with the same dimensions. The commutative property states that changing the order of the addition or subtraction of two matrices lead to the same result. For the associative property, changing what matrices you add or subtract one will lead to the same answer. There are also matrix addition properties for identity and <a href="[[glossary.html|{"keyword":"Zero matrix"}]]">zero matrices</a> as well. Adding a zero matrix with another matrix (call it A) will give back A. Multiplying an <a href='[[glossary.html|{"keyword":"Identity matrix"}]]'>identity matrix</a> with another matrix (call it B) will give back B.

Rules for matrix addition and practice questions