2.1 Vectors and Linear Equations

• Row pic

• Column pic

• Matrix multiplication

2.2 The Idea of Elimination

• Elimination

2.3 Elimination Using Matrices

• Special Matrix

2.4 Rules for Matrix Operations

• Block Matrices

2.5 Inverse Matrices

If $A$ is invertible, then $Ax = 0$ can only have the zero solution $x = A^{-1}0 = 0$

• Inverse Matrices

2.6 Elimination = Factorization: A = LU

• LU Elimination
• The Cost of Elimination