MATH-250 Linear Algebra

Students will develop skills in the basic concepts of linear algebra. These skills will cover areas such as vector spaces, systems of linear equations and matrices, determinants, similar matrices, diagonalizations, linear transformations, eigenvalues and eigenvectors, inner product spaces, quadratic forms, and complex vector spaces. Use of MATLAB, the computer algebra system, is required. Calculators are not permitted.

Credits

4

Prerequisite

MATH-181 or equivalent

Hours Weekly

4 hours weekly

Course Objectives

1. 1. Solve systems of linear equations using matrices with elementary row operations.
2. 2. Basic vector arithmetic; calculate vector sums, differences, scalar products and inner
   products; calculate projections.
3. 3. Use the basic rules of matrix arithmetic and algebra to calculate a product of a scalar and a
   matrix, matrix sum, a matrix inverse, a matrix transpose, etc.
4. 4. Use the basic concepts of vectors and vector spaces to solve certain matrix equations. AX=B
   
5. 5. Explore matrix factorizations e.g. LU and diagonalizations of square matrices.
   
6. 6. Identify fundamental vector spaces and subspaces.
7. 7. Find bases and coordinate vectors in general vector spaces.
8. 8. Use concept of a linear transformation by applying it to geometry and to differentiation;
   develop matrix representations of linear transformations, calculate associated eigenvalues
   and eigenvectors.
9. 9. Calculate the determinant of a matrix and use it when solving a system of linear equations.
   
10. 10. Calculate orthogonal and orthonormal bases in vector spaces.
    
11. 11. Solve applications dealing with quadratic forms.
12. 12. Use complex numbers in both complex matrix spaces and complex vector spaces.

Course Objectives

1. 1. Solve systems of linear equations using matrices with elementary row operations.
2. 2. Basic vector arithmetic; calculate vector sums, differences, scalar products and inner
   products; calculate projections.
3. 3. Use the basic rules of matrix arithmetic and algebra to calculate a product of a scalar and a
   matrix, matrix sum, a matrix inverse, a matrix transpose, etc.
4. 4. Use the basic concepts of vectors and vector spaces to solve certain matrix equations. AX=B
   
5. 5. Explore matrix factorizations e.g. LU and diagonalizations of square matrices.
   
6. 6. Identify fundamental vector spaces and subspaces.
7. 7. Find bases and coordinate vectors in general vector spaces.
8. 8. Use concept of a linear transformation by applying it to geometry and to differentiation;
   develop matrix representations of linear transformations, calculate associated eigenvalues
   and eigenvectors.
9. 9. Calculate the determinant of a matrix and use it when solving a system of linear equations.
   
10. 10. Calculate orthogonal and orthonormal bases in vector spaces.
    
11. 11. Solve applications dealing with quadratic forms.
12. 12. Use complex numbers in both complex matrix spaces and complex vector spaces.