The main goal of this course is to provide the basic concepts of linear algebra. The mathematical background obtained in this course will be utilized in other undergraduate courses. The students will acquire the techniques to solve systems of linear equations via matrices and understand vector spaces. In terms of thorough knowledge of matrices, matrix operations, determinants, projections, general understanding of vector spaces, the students will be ready to study and understand various applications of these concepts.
On successful completion of this course, the students should be able to
1) Think in abstract and general terms
2) Determine whether the solution to a linear system is unique or not
3) Solve a linear system
4) Know basic concepts about matrices
5) Perform basic operations on matrices such as the calculation of the matrix inverse
6) Express a determinant as a cofactor expansion, evaluate determinants
7) Understand Euclidean and general vector spaces and related notions such as norms, dot product, projections, basis, linear independence, coordinates, dimensions, rank, nullity
8) Know what a transformation is, properties of transformations and the geometry of matrix operations
9) Recall basic definitions of an eigenvalue, eigenvector
10) Able to determine whether a matrix is diagonalizale
11) Know inner products, orthogonality
12) Able to use Gram-Schmidt Process, decomposion methods and express the solution of a least-squares problem as the solution of a linear system
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