University Linear Algebra Worksheets

Which sets match your course code

University Linear Algebra is not one course with one number. The material is split across different courses in the public calendars of Montreal universities, and each orders and weights it its own way. Find your code below for the sets that cover its material, then check your own outline for what your exam includes.

• MAST 234 — Vector Spaces and Subspaces, Span and Linear Independence, Basis, Dimension and Coordinates, Rank and the Fundamental Subspaces, Linear Transformations, Change of Basis and Matrix Representations, Eigenvalues and Diagonalization
• MAST 235 — Eigenvalues and Diagonalization, Inner Products and Orthogonality, Least Squares
• MAT1250 — Vector Spaces and Subspaces, Span and Linear Independence, Basis, Dimension and Coordinates, Rank and the Fundamental Subspaces, Linear Transformations, Change of Basis and Matrix Representations, Eigenvalues and Diagonalization, Least Squares
• MAT1260 — Vector Spaces and Subspaces, Span and Linear Independence, Basis, Dimension and Coordinates, Linear Transformations, Change of Basis and Matrix Representations, Eigenvalues and Diagonalization, Inner Products and Orthogonality, Least Squares
• MAT1600 — Vector Spaces and Subspaces, Linear Transformations, Eigenvalues and Diagonalization, Inner Products and Orthogonality
• MAT472 — Vector Spaces and Subspaces, Basis, Dimension and Coordinates, Linear Transformations, Change of Basis and Matrix Representations, Eigenvalues and Diagonalization
• MATH 133 — Vector Spaces and Subspaces, Span and Linear Independence, Basis, Dimension and Coordinates, Linear Transformations, Eigenvalues and Diagonalization
• MATH 204 — Vector Spaces and Subspaces, Span and Linear Independence, Basis, Dimension and Coordinates, Linear Transformations, Eigenvalues and Diagonalization
• MATH 223 — Vector Spaces and Subspaces, Linear Transformations, Change of Basis and Matrix Representations, Eigenvalues and Diagonalization, Inner Products and Orthogonality, Least Squares
• MATH 251 — Vector Spaces and Subspaces, Span and Linear Independence, Basis, Dimension and Coordinates, Rank and the Fundamental Subspaces, Linear Transformations, Change of Basis and Matrix Representations, Eigenvalues and Diagonalization
• MATH 252 — Eigenvalues and Diagonalization, Inner Products and Orthogonality, Least Squares

Notes and unit tests — in the bundle

Every University Linear Algebra unit has three printable documents, not one: the practice worksheet above, which is free, and two that come with the University Linear Algebra bundle — a set of unit notes stating everything the unit defines, and a full end-of-unit test to sit closed-book. See what each one covers:

What the 9 sets of unit notes cover  What the 9 unit tests look like

What University Linear Algebra covers

CEGEP Linear Algebra lives in the plane and in space. This course leaves them. A vector can have five coordinates, or be a polynomial, a matrix or a function, and the same questions are asked of all of them: does this set span, is it independent, is it a basis, what are the coordinates of this vector? Most of the marks in the first half of the course are in deciding which of those questions you are being asked — the row reduction that answers it is the part you already know.

The middle of the course turns matrices into functions. A matrix has a null space, a column space and a row space, and a linear transformation has a kernel and a range; the rank theorem ties their dimensions together, and a change of basis rewrites one map as many matrices. The last three sets are the payoff: eigenvalues and diagonalization, which find the basis in which a map is simplest; inner products and orthogonal bases, which make coordinates free; and projections, least squares and the orthogonal diagonalization of a symmetric matrix.

The course stands on CEGEP Linear Algebra. Matrix arithmetic, row reduction, inverses, determinants, and vectors, lines and planes in space are not re-taught here — they are in that course's sets. Scalars are real throughout. The courses that carry this material at university split it differently: some are one term that ends at diagonalization, some are a pair of terms with orthogonality in the second, and one covers the linear algebra alongside multivariable calculus. The list of course codes on this page says which sets each one covers.