Topic: Proof Strategies in Linear Algebra

Kernel and Image Subspace Proofs

Injectivity and Surjectivity Through Kernel and Image

Independence Proofs from the Zero-Combination Equation

Extracting Dependence Relations from Row Reduction

Establishing a Basis by Independence and Spanning

Dimension Counts for Independence and Spanning

Counterexamples to Independence and Spanning Claims

Counterexamples to Subspace and Linearity Claims

Contraposition and Contradiction in Linear Algebra Proofs

Common Errors in Dimension and Pivot Arguments