Linear Algebra curriculum

Start with 18.06 Linear Algebra and OpenStax Math. Take notes until you can explain: Represent systems as equations, vector combinations, and augmented matrices.

Do the first sequenced checks until the definitions, vocabulary, and setup are correct without hints.

Produce the assignment artifact, then pass the application and analysis checks tied to: Solve a three-equation system and describe the solution as a point, line, plane, or empty set.

Any miss becomes an error-log entry, a clean redo, and one nearby transfer problem before advancing.

Bring your attempted work, the exact missed check, and one question about: Interpret span and solution sets geometrically.

Start with 18.06 Linear Algebra and OpenStax Math. Take notes until you can explain: Use row operations, echelon form, pivots, rank, and LU factorization.

Do the first sequenced checks until the definitions, vocabulary, and setup are correct without hints.

Produce the assignment artifact, then pass the application and analysis checks tied to: Reduce a matrix by hand, identify pivot columns, and state rank and free variables.

Any miss becomes an error-log entry, a clean redo, and one nearby transfer problem before advancing.

Bring your attempted work, the exact missed check, and one question about: Detect inconsistent and dependent systems.

Start with 18.06 Linear Algebra and OpenStax Math. Take notes until you can explain: Use subspace tests for column spaces, null spaces, and spans.

Do the first sequenced checks until the definitions, vocabulary, and setup are correct without hints.

Produce the assignment artifact, then pass the application and analysis checks tied to: Determine whether three proposed sets are subspaces and justify each conclusion.

Any miss becomes an error-log entry, a clean redo, and one nearby transfer problem before advancing.

Bring your attempted work, the exact missed check, and one question about: Move between set notation, equations, and bases.

Start with 18.06 Linear Algebra and OpenStax Math. Take notes until you can explain: Test linear independence and construct bases.

Do the first sequenced checks until the definitions, vocabulary, and setup are correct without hints.

Produce the assignment artifact, then pass the application and analysis checks tied to: Find bases for the column space and null space of one matrix and explain the dimensions.

Any miss becomes an error-log entry, a clean redo, and one nearby transfer problem before advancing.

Bring your attempted work, the exact missed check, and one question about: Use dimension to reason about coordinates and redundancy.

Start with 18.06 Linear Algebra and OpenStax Math. Take notes until you can explain: Represent transformations with matrices.

Do the first sequenced checks until the definitions, vocabulary, and setup are correct without hints.

Produce the assignment artifact, then pass the application and analysis checks tied to: Build a matrix for a geometric transformation and predict what happens to several vectors.

Any miss becomes an error-log entry, a clean redo, and one nearby transfer problem before advancing.

Bring your attempted work, the exact missed check, and one question about: Use kernels, images, composition, invertibility, and change of basis.

Start with 18.06 Linear Algebra and OpenStax Math. Take notes until you can explain: Use dot products, projections, orthogonal bases, and Gram-Schmidt.

Do the first sequenced checks until the definitions, vocabulary, and setup are correct without hints.

Produce the assignment artifact, then pass the application and analysis checks tied to: Fit a least-squares line from matrix notation and explain why the residual is orthogonal.

Any miss becomes an error-log entry, a clean redo, and one nearby transfer problem before advancing.

Bring your attempted work, the exact missed check, and one question about: Fit least-squares models and interpret residuals.

Start with 18.06 Linear Algebra and OpenStax Math. Take notes until you can explain: Compute determinants and eigenvalues.

Do the first sequenced checks until the definitions, vocabulary, and setup are correct without hints.

Produce the assignment artifact, then pass the application and analysis checks tied to: Diagonalize a small matrix when possible and use it to compute a matrix power.

Any miss becomes an error-log entry, a clean redo, and one nearby transfer problem before advancing.

Bring your attempted work, the exact missed check, and one question about: Use diagonalization to understand repeated transformations.

Start with 18.06 Linear Algebra and OpenStax Math. Take notes until you can explain: Apply linear algebra to graphs, Markov chains, data compression, and differential equations.

Do the first sequenced checks until the definitions, vocabulary, and setup are correct without hints.

Produce the assignment artifact, then pass the application and analysis checks tied to: Complete an application brief with the matrix model, assumptions, computation, and interpretation.

Any miss becomes an error-log entry, a clean redo, and one nearby transfer problem before advancing.

Bring your attempted work, the exact missed check, and one question about: Write short proofs from definitions.