Linear Algebra Course
A concise, structured course covering core linear algebra concepts with worked examples and progressive exercises.
Course Structure
9 comprehensive lessons with prerequisites, objectives, and examples
Learn by Doing
Each lesson includes worked examples and practice problems
Progressive Difficulty
Build from fundamentals to advanced topics step by step
Permutations and Inverse Definition
Condition for invertibility: nonzero determinant. Formula for inverse of $\begin{bmatrix}a & b\\c & d\end{bmatrix}$ is $\frac{1}{ad-bc}\begin{bmatrix}d & -b\\-c & a\end{bmatrix}$.
Inverse of a 2x2 matrix
Condition for invertibility: nonzero determinant. Formula for inverse of $\begin{bmatrix}a & b\\c & d\end{bmatrix}$ is $\frac{1}{ad-bc}\begin{bmatrix}d & -b\\-c & a\end{bmatrix}$.
Inverse of a 3x3 matrix
Condition for invertibility: nonzero determinant. Formula for inverse of $\begin{bmatrix}a & b\\c & d\end{bmatrix}$ is $\frac{1}{ad-bc}\begin{bmatrix}d & -b\\-c & a\end{bmatrix}$.