LaTeX Matrices: Create 2x2, 3x3, 4x4 and Determinants

Creating Matrices in LaTeX

Matrices are essential for linear algebra, physics, and engineering. Here's how to create them perfectly in LaTeX.

Basic Matrix Syntax

Use the amsmath package and matrix environments:

\usepackage{amsmath}

Matrix with Parentheses (pmatrix)

$\begin{pmatrix} a & b \\ c & d \end{pmatrix}$

Creates a 2x2 matrix with round brackets.

Matrix with Square Brackets (bmatrix)

$\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix}$

Creates a 3x3 matrix with square brackets.

2x2 Matrix

$A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$

2x2 Determinant

$\det(A) = \begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad - bc$

3x3 Matrix

$B = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix}$

3x3 Determinant

Use vmatrix for determinant notation:

$\begin{vmatrix} a & b & c \\ d & e & f \\ g & h & i \end{vmatrix}$

4x4 Matrix

$C = \begin{bmatrix} c_{11} & c_{12} & c_{13} & c_{14} \\ c_{21} & c_{22} & c_{23} & c_{24} \\ c_{31} & c_{32} & c_{33} & c_{34} \\ c_{41} & c_{42} & c_{43} & c_{44} \end{bmatrix}$

All Matrix Bracket Types

- matrix — no brackets - pmatrix — parentheses ( ) - bmatrix — square brackets [ ] - Bmatrix — curly braces { } - vmatrix — vertical bars | | (determinant) - Vmatrix — double bars || ||

Special Matrices

Identity Matrix

$I = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$

Diagonal Matrix

$D = \begin{bmatrix} d_1 & 0 & 0 \\ 0 & d_2 & 0 \\ 0 & 0 & d_3 \end{bmatrix}$

Zero Matrix

$O = \begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix}$

Augmented Matrices

For systems of equations, use array with a divider:

$\left[\begin{array}{ccc|c} 1 & 2 & 3 & 4 \\ 5 & 6 & 7 & 8 \\ 9 & 10 & 11 & 12 \end{array}\right]$

Large Matrices with Dots

$\begin{bmatrix} a_{11} & \cdots & a_{1n} \\ \vdots & \ddots & \vdots \\ a_{m1} & \cdots & a_{mn} \end{bmatrix}$

Use \cdots (horizontal), \vdots (vertical), \ddots (diagonal).

Matrix Operations

Multiplication

$AB = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \begin{bmatrix} e & f \\ g & h \end{bmatrix}$

Transpose

$A^T = \begin{bmatrix} a & c \\ b & d \end{bmatrix}$

Inverse

$A^{-1} = \frac{1}{ad-bc} \begin{bmatrix} d & -b \\ -c & a \end{bmatrix}$

Column and Row Vectors

Column Vector

$\mathbf{v} = \begin{bmatrix} v_1 \\ v_2 \\ v_3 \end{bmatrix}$

Row Vector

$\mathbf{u} = \begin{bmatrix} u_1 & u_2 & u_3 \end{bmatrix}$

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