Goal: see matrices as geometric machines, not only as arrays to row-reduce.
- Linear algebra pillar for the landscape.
- Master vocabulary: vector, span, linear independence, basis, linear map, matrix.
- Practice: interpret columns of a matrix as images of basis vectors.
- Eigenvalues in plain language, then eigenvalue / eigenvector / eigenspace.
- Optional bridge: Multivariable intro (gradients as linear approximations).
Pitfall. Do not rush to determinants as “the formula.” Learn when a map collapses volume and why singularity blocks solving A x = b uniquely.