Math Pi

Matrices is a branch of algebra. These classes cover basics of matrices, identities of matrices, and most used concepts of matrices with detailed explanation and number of examples.

Matrices Basics

Introduction to Matrices

Types of Matrices

Square Matrix Rectangular Matrix Diagonal Matrix Identity Matrix Zero Matrix Upper Triangular Matrix Lower Triangular Matrix Row Matrix Column Matrix

Matrix Operations

Matrix Addition Matrix Subtraction Matrix Multiplication Matrix Transpose Matrix Determinant Matrix Rank Matrix Inverse

Matrix Addition Concepts

1x1 Matrix Addition 2x2 Matrix Addition 3x3 Matrix Addition Solve Matrix Addition \( \begin{bmatrix}1 & 2\\3 & 4\end{bmatrix} + \begin{bmatrix}5 & 6\\7 & 8\end{bmatrix} \)Solve Matrix Addition \( \begin{bmatrix}1 & 2 & 3\\4 & 5 & 6\end{bmatrix} + \begin{bmatrix}7 & 8 & 9\\10 & 11 & 12\end{bmatrix} \)Solve Matrix Addition \( \begin{bmatrix}1 & 2 & 3\\4 & 5 & 6\\7 & 8 & 9\end{bmatrix} +\)\( \begin{bmatrix}10 & 11 & 12\\13 & 14 & 15\\16 & 17 & 18\end{bmatrix} \)

Matrix Subtraction Concepts

1x1 Matrix Subtraction 2x2 Matrix Subtraction 3x3 Matrix Subtraction Solve Matrix Subtraction \( \begin{bmatrix}1 & 2\\3 & 4\end{bmatrix} - \begin{bmatrix}5 & 6\\7 & 8\end{bmatrix} \)Solve Matrix Subtraction \( \begin{bmatrix}1 & 2 & 3\\4 & 5 & 6\end{bmatrix} - \begin{bmatrix}7 & 8 & 9\\10 & 11 & 12\end{bmatrix} \)Solve Matrix Subtraction \( \begin{bmatrix}1 & 2 & 3\\4 & 5 & 6\\7 & 8 & 9\end{bmatrix} -\)\( \begin{bmatrix}10 & 11 & 12\\13 & 14 & 15\\16 & 17 & 18\end{bmatrix} \)

Matrix Multiplication Concepts

1x1 Matrix Multiplication 2x2 Matrix Multiplication 3x3 Matrix Multiplication Solve Matrix Multiplication \( \begin{bmatrix}1 & 2\\3 & 4\end{bmatrix} \times \begin{bmatrix}5 & 6\\7 & 8\end{bmatrix} \)Solve Matrix Multiplication \( \begin{bmatrix}1 & 2 & 3\\4 & 5 & 6\\7 & 8 & 9\end{bmatrix} \times \)\( \begin{bmatrix}10 & 11 & 12\\13 & 14 & 15\\16 & 17 & 18\end{bmatrix} \)

Matrix Theorems

Rank Theorem

Matrix Determinant Concepts

Matrix Determinant Using Minors and Cofactors Matrix Determinant using Sarrus' Rule Example 1: Solve Determinant of 4x4 Matrix using Minors and Cofactors

Matrix Inverse Concepts

Matrix Inverse Rules Example for \( AI = IA = A \)Example for \( AA^{-1} = A^{-1}A = I \)Example for \( (A^{-1})^{-1} = A \)Example for \( ( AB )^{-1} = B^{-1}A^{-1} \)Example for \( (ABC)^{-1} = C^{-1}B^{-1}A^{-1} \)Example for \( (A')^{-1} = (A^{-1})' \)Matrix Inverse Using Gauss-Jordan Elimination

{ "title": "Matrices", "slug": "matrices", "description": "Matrices is a branch of algebra. These classes cover basics of matrices, identities of matrices, and most used concepts of matrices with detailed explanation and number of examples.", "linksHtml": "<div class=\"section\"><h2>Matrices Basics</h2><a href=\"/matrices/matrix-introduction\">Introduction to Matrices</a></div><div class=\"section\"><h2>Types of Matrices</h2><a href=\"/matrices/square-matrix\">Square Matrix</a><a href=\"/matrices/rectangular-matrix\">Rectangular Matrix</a><a href=\"/matrices/diagonal-matrix\">Diagonal Matrix</a><a href=\"/matrices/identity-matrix\">Identity Matrix</a><a href=\"/matrices/zero-matrix\">Zero Matrix</a><a href=\"/matrices/upper-triangular-matrix\">Upper Triangular Matrix</a><a href=\"/matrices/lower-triangular-matrix\">Lower Triangular Matrix</a><a href=\"/matrices/row-matrix\">Row Matrix</a><a href=\"/matrices/column-matrix\">Column Matrix</a></div><div class=\"section\"><h2>Matrix Operations</h2><a href=\"/matrices/matrix-addition\">Matrix Addition</a><a href=\"/matrices/matrix-subtraction\">Matrix Subtraction</a><a href=\"/matrices/matrix-multiplication\">Matrix Multiplication</a><a href=\"/matrices/matrix-transpose\">Matrix Transpose</a><a href=\"/matrices/matrix-determinant\">Matrix Determinant</a><a href=\"/matrices/matrix-rank\">Matrix Rank</a><a href=\"/matrices/matrix-inverse\">Matrix Inverse</a></div><div class=\"section\"><h2>Matrix Addition Concepts</h2><a href=\"/matrices/1-1-matrix-addition\">1x1 Matrix Addition</a><a href=\"/matrices/2-2-matrix-addition\">2x2 Matrix Addition</a><a href=\"/matrices/3-3-matrix-addition\">3x3 Matrix Addition</a><a href=\"/matrices/matrix-addition-2x2-example-1\">Solve Matrix Addition \\( \\begin{bmatrix}1 & 2\\\\3 & 4\\end{bmatrix} + \\begin{bmatrix}5 & 6\\\\7 & 8\\end{bmatrix} \\)</a><a href=\"/matrices/matrix-addition-2x3-example-1\">Solve Matrix Addition \\( \\begin{bmatrix}1 & 2 & 3\\\\4 & 5 & 6\\end{bmatrix} + \\begin{bmatrix}7 & 8 & 9\\\\10 & 11 & 12\\end{bmatrix} \\)</a><a href=\"/matrices/matrix-addition-3x3-example-1\">Solve Matrix Addition \\( \\begin{bmatrix}1 & 2 & 3\\\\4 & 5 & 6\\\\7 & 8 & 9\\end{bmatrix} +\\)\\( \\begin{bmatrix}10 & 11 & 12\\\\13 & 14 & 15\\\\16 & 17 & 18\\end{bmatrix} \\)</a></div><div class=\"section\"><h2>Matrix Subtraction Concepts</h2><a href=\"/matrices/1-1-matrix-subtraction\">1x1 Matrix Subtraction</a><a href=\"/matrices/2-2-matrix-subtraction\">2x2 Matrix Subtraction</a><a href=\"/matrices/3-3-matrix-subtraction\">3x3 Matrix Subtraction</a><a href=\"/matrices/matrix-subtraction-2x2-example-1\">Solve Matrix Subtraction \\( \\begin{bmatrix}1 & 2\\\\3 & 4\\end{bmatrix} - \\begin{bmatrix}5 & 6\\\\7 & 8\\end{bmatrix} \\)</a><a href=\"/matrices/matrix-subtraction-2x3-example-1\">Solve Matrix Subtraction \\( \\begin{bmatrix}1 & 2 & 3\\\\4 & 5 & 6\\end{bmatrix} - \\begin{bmatrix}7 & 8 & 9\\\\10 & 11 & 12\\end{bmatrix} \\)</a><a href=\"/matrices/matrix-subtraction-3x3-example-1\">Solve Matrix Subtraction \\( \\begin{bmatrix}1 & 2 & 3\\\\4 & 5 & 6\\\\7 & 8 & 9\\end{bmatrix} -\\)\\( \\begin{bmatrix}10 & 11 & 12\\\\13 & 14 & 15\\\\16 & 17 & 18\\end{bmatrix} \\)</a></div><div class=\"section\"><h2>Matrix Multiplication Concepts</h2><a href=\"/matrices/1-1-matrix-multiplication\">1x1 Matrix Multiplication</a><a href=\"/matrices/2-2-matrix-multiplication\">2x2 Matrix Multiplication</a><a href=\"/matrices/3-3-matrix-multiplication\">3x3 Matrix Multiplication</a><a href=\"/matrices/matrix-multiplication-2x2-example-1\">Solve Matrix Multiplication \\( \\begin{bmatrix}1 & 2\\\\3 & 4\\end{bmatrix} \\times \\begin{bmatrix}5 & 6\\\\7 & 8\\end{bmatrix} \\)</a><a href=\"/matrices/matrix-multiplication-3x3-example-1\">Solve Matrix Multiplication \\( \\begin{bmatrix}1 & 2 & 3\\\\4 & 5 & 6\\\\7 & 8 & 9\\end{bmatrix} \\times \\)\\( \\begin{bmatrix}10 & 11 & 12\\\\13 & 14 & 15\\\\16 & 17 & 18\\end{bmatrix} \\)</a></div><div class=\"section\"><h2>Matrix Theorems</h2><a href=\"/matrices/rank-theorem\">Rank Theorem</a></div><div class=\"section\"><h2>Matrix Determinant Concepts</h2><a href=\"/matrices/matrix-determinant-using-minors-and-cofactors\">Matrix Determinant Using Minors and Cofactors</a><a href=\"/matrices/matrix-determinant-using-sarrus-rule\">Matrix Determinant using Sarrus' Rule</a><a href=\"/matrices/determinant-of-4-4-matrix-using-minors-and-cofactors-1\">Example 1: Solve Determinant of 4x4 Matrix using Minors and Cofactors</a></div><div class=\"section\"><h2>Matrix Inverse Concepts</h2><a href=\"/matrices/matrix-inverse-rules\">Matrix Inverse Rules</a><a href=\"/matrices/example-for-matrix-a-inverse-inverse\">Example for \\( AI = IA = A \\)</a><a href=\"/matrices/example-for-matrix-a-inverse-inverse\">Example for \\( AA^{-1} = A^{-1}A = I \\)</a><a href=\"/matrices/example-for-matrix-a-inverse-inverse\">Example for \\( (A^{-1})^{-1} = A \\)</a><a href=\"/matrices/example-for-matrix-a-b-inverse\">Example for \\( ( AB )^{-1} = B^{-1}A^{-1} \\)</a><a href=\"/matrices/example-for-matrix-a-b-c-inverse\">Example for \\( (ABC)^{-1} = C^{-1}B^{-1}A^{-1} \\)</a><a href=\"/matrices/example-for-matrix-a-transpose-inverse\">Example for \\( (A')^{-1} = (A^{-1})' \\)</a><a href=\"/matrices/matrix-inverse-using-gauss-jordan-elimination\">Matrix Inverse Using Gauss-Jordan Elimination</a></div>" }