🗺️ Chapter Roadmap
1 What is a Matrix?
A Matrix is an arrangement of numbers into Rows (horizontal lines) and Columns (vertical lines) enclosed within square brackets [ ].
The Order of this matrix is 2 × 2 (Rows × Columns).
2 Common Types
Row Matrix
Has only one single row.
Column Matrix
Has only one single column.
Square Matrix
Rows = Columns (e.g. 2x2, 3x3).
Identity Matrix (I)
1s on diagonal, 0s elsewhere.
[ 0 1 ]
Null (Zero) Matrix
Every single element is zero.
[ 0 0 ]
3 Matrix Operations
Addition & Subtraction
You can only add or subtract matrices if they have the same order. Just add/subtract the matching spots.
Transpose (AT)
The Transpose is found by switching all Rows into Columns.
[ 3 4 ]
[ 2 4 ]
4 Determinant & Adjoint
The determinant is a single number value of a square matrix. For a 2×2 matrix, use the Cross-Minus rule.
Matrix A
1. Determinant |A|
Multiply diagonals and subtract.
If |A| = 0. This matrix has no inverse.
If |A| ≠ 0. This matrix can be inverted.
5 Inverse of a 2x2 Matrix
The Inverse (A−1) is like the reciprocal (1/x) for matrices. To find it, you need the Adjoint and the Determinant.
How to find Adjoint (Adj A)?
- Swap a and d.
- Change signs of b and c (make them negative/positive).