📘 Chapter 1: Introduction to Matrices
A matrix is an array of numbers arranged in rows and columns, like this:
\[ A = \begin{bmatrix} a_{11} & a_{12} & \cdots & a_{1n} \\ a_{21} & a_{22} & \cdots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m1} & a_{m2} & \cdots & a_{mn} \end{bmatrix} \]🧩 Types of Matrices
- Row Matrix: Single row
- Column Matrix: Single column
- Square Matrix: Same number of rows and columns
- Zero Matrix: All elements are zero
🔄 Matrix Operations
Basic matrix operations include addition, multiplication, scalar multiplication, etc.
\[ A + B = \begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix} + \begin{bmatrix}5 & 6 \\ 7 & 8\end{bmatrix} = \begin{bmatrix}6 & 8 \\ 10 & 12\end{bmatrix} \]📊 Examples
Given:
\[ A = \begin{bmatrix}2 & 3 \\ 4 & 5\end{bmatrix} \Rightarrow A^T = \begin{bmatrix}2 & 4 \\ 3 & 5\end{bmatrix} \]📝 Practice
Compute the sum:
\[ \begin{bmatrix}3 & 1 \\ 0 & 2\end{bmatrix} + \begin{bmatrix}6 & 2 \\ 1 & 3\end{bmatrix} \]