These study notes will help you understand "Matrices & Determinants" from the very beginning. We'll use simple words and examples.
Matrices & Determinants: Study Notes
Part 1: Matrices
1. What is a Matrix?
Imagine you have some numbers you want to keep organized in a neat box. A matrix is just like that: a rectangular arrangement of numbers (or functions).
- It helps us organize data.
- It looks like a table.
Example: Imagine marks of two students in two subjects:
Student 1: Math 80, Physics 75 Student 2: Math 90, Physics 85
We can put this in a matrix: $$ A = \begin{bmatrix} 80 & 75 \ 90 & 85 \end{bmatrix} $$
The numbers inside are called elements.
2. Order of a Matrix
The "order" tells us the size of the matrix. It's always (number of rows) $\times$ (number of columns).
- Rows go across (horizontal).
- Columns go up and down (vertical).
Example: $$ A = \begin{bmatrix} 80 & 75 \ 90 & 85 \end{bmatrix} $$ This matrix has 2