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APSC 174 Introduction To Linear Algebra Units: 3.30
Systems of linear equations; real vectors spaces and subspaces; linear combinations and linear spans; linear dependence and linear independence; applications to systems of linear equations and their solution via Gaussian elimination; bases and dimension of real vector spaces; linear transformations, range, kernel and Rank-Nullity theorem; matrix representation of a linear transformation; composition of linear transformations and matrix multiplication; invertible matrices and determinants; eigenvalues and eigenvectors of square matrices. Applications of the course material to engineering systems are illustrated.
(Lec: 2.8, Lab: 0, Tut: 0.5)
(Lec: 2.8, Lab: 0, Tut: 0.5)
Offering Term: WS
CEAB Units:
Mathematics 40
Natural Sciences 0
Complementary Studies 0
Engineering Science 0
Engineering Design 0
Course Equivalencies: MATH 110B/112 / APSC 174
Offering Faculty: Smith Engineering
Course Learning Outcomes:
- Solve parametrized and unparametrized systems of linear equations using Gaussian elimination and back substitution by applying elementary row operations on an augmented matrix; for parametrized systems also determine the number of solutions as a function of the parameter.
- Perform basic matrix algebraic operations (addition, scaling, multiplication), and compute and utilize properties of the determinant of a real n x n matrix (including using it to assess whether a matrix is invertible).
- Explain the mathematical concept of a real vector space, and determine whether a given subset of a vector space is a vector subspace by working with both the usual Euclidean space Rn and other vector spaces.
- Demonstrate an understanding of linear combination, linear dependence, linear span, basis and dimension by: i) determining whether a given vector in is the linear span of a family of vectors and whether that family of vectors is linearly independent, ii) computing a basis for a given vector space and its dimension.
- Define a linear mapping between vector spaces and determine if a given mapping is linear.
- Define the kernel and image of a linear mapping, compute them for a given real matrix, and explain how they are related to the column vectors of that matrix.
- Define eigenvalues, eigenspaces and eigenvectors for a given vector space endomorphism and compute them for a real n x n matrix.
- Prove linear algebraic results for general vector spaces with mathematical reasoning and in precise mathematical language, combining concepts such as vector subspaces, linear span, linear independence, linear mapping, and eigenvalues/eigenspaces/eigenvectors.