1. Develop algebraic skills and use algorithmic techniques essential for the study of aspects such as matrix algebra, vector spaces, systems of linear equation, eigenvalues and eigenvectors, orthogonality and diagonalization.
2. Develop spatial reasoning and utilize geometric properties and strategies to model and solve problems as well as view the solution in R2 and R3 and conceptually extend these results to higher dimensions
3. Construct mathematical arguments and understand proofs and concepts that involve elements of introductory linear algebra.
4. Be aware of computational packages and programming languages, where appropriate, that would facilitate them in solving problems and presenting the related solutions.
5. Communicate linear algebra statements, ideas and results, both verbally and in writing, with the correct use of mathematical definitions, terminology and notation.
Course Content (Syllabus)
Matrix algebra. Determinants. Solution of linear systems. Vector spaces (linear dependence and independence, basis, dimension). Linear and bilinear transformations. Application of vector spaces to linear systems (image, kernel, rank, nullity). Orthogonality. Eigenvalues, eigenvectors and their applications. Vectors and their algebra. Euclidean spaces RN. Outer and mixed product in R3. Equations of lines and planes in R3. Relative positions of lines and planes. Surfaces. Sphere. Classification of 2nd order curves in the plane and surfaces in space.
Matrices, Linear Systems, Vector Spaces, Eigenvalues, Analytic Geometry.