Linear Algebra I
Vectors, matrices and the structure of linear systems.
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Vectors and Matrix Operations
Vector arithmetic, matrix algebra, and transpose properties.
Linear Systems and Gaussian Elimination
Row reduction, echelon forms, rank, and solution sets.
Matrix Inverses and Determinants
Invertibility, cofactor expansion, and determinant properties.
Vector Spaces and Subspaces
Span, null/column space, and subspace tests.
Linear Independence, Basis and Dimension
Coordinates, basis construction, and the rank-nullity theorem.
Linear Transformations
Matrix representations, kernel and image, and geometry of transformations.
Eigenvalues and Eigenvectors
Characteristic polynomials, eigenspaces, and a first look at diagonalization.
Orthogonality and Projections
Dot products, orthogonal sets, projections, and least squares.