Math 201 – Linear Algebra, Winter 2019


Instructor: Anatolii Grinshpan.
Office hours:  MW 12-1 and R 2-3, Math Resource Center.

Course information    Academic calendar     

Week 1. Introduction to the course. Gaussian elimination. Leading and free variables. Example.

              Reduced row echelon form. Rank. Newton interpolation. Tall, long, square.

Reading: 1.1, 1.2. Homework 1 (answers). Fangcheng. Uniqueness of RREF.


Week 2. Homework discussion. Quiz 1 (Gauss-Jordan elimination). Kronecker-Capelli theorem.

              Vectors and vector arithmetic. Homogeneous and nonhomogeneous systems. Matrix-vector product.         

Reading: 1.3. Homework 2 (answers).


Week 3.  No classes.


Week 4. Linear transformations and matrices. Quiz 2 (matrix-vector product).

              Projections, reflections, rotations, and their matrices. Orthogonal projection in the plane.

Reading 2.1, 2.2. Homework 3 (answers).


Week 5.  Matrix multiplication and inversion. Example. Quiz 3 (linear transformations).

               Midterm 1 (1.1-1.3, 2.1-2.4).

Reading 2.3, 2.4. Homework 4 (answers).


Week 6.  Span of vectors. Kernel and image of a matrix. Subspaces of the Euclidean space.

               Quiz 4 (kernel and image). Vectors relations and row/column operations. Notes. Redundancy and linear independence.

Reading: 3.1, 3.2. Homework 5 (answers).  Characterizations of linear (in)dependence.


Week 7.  Basis and dimension. Basis for the kernel. Basis for the image. Rank-nullity theorem.

              Quiz 5 (linear independence). Coordinates. Matrix with respect to a given basis.

Reading: 3.3, 3.4. Homework 6 (answers). Change of basis in the plane.

Saturday class: 10 AM – Noon, Randell 121. Lecture notes.


Week 8.  Matrix transpose. Orthonormal bases. Orthogonal projection onto a subspace.

               Orthogonalization of vectorsOrthogonal matrices. Homogeneous equations and orthogonality.

Reading: 5.1-5.3. Homework 7 (answers).


Week 9.  Midterm 2 (3.1-3.4, 5.1-5.3). Determinants. Cramer’s rule.

Reading: 6.1-6.3. Homework 8 (answers). Notes on determinants.


Week 10. Eigenvalues and eigenvectors. Eigenspaces. Examples. Algebraic and geometric multiplicities.

                Quiz 6 (eigenvalues and eigenvectors). Eigenbases and diagonalization. Examples. 

Reading: 7.1-7.3. Homework 9 (answers). Cross-product transformation.


March 20. Questions session: 10 AM-Noon, Pearl 303.

                  Office hours: 1-3PM, Korman 207.


March 21. Final exam: 10:30-12:30, Stratton 113. (answer key)