Accelerated College Program

Courses - Math 254

Student Learning Outcomes for Math 254
  1. Solve systems of linear equations using several algebraic methods.
  2. Construct and apply special matrices, such as symmetric, skew-symmetric, diagonal, upper triangular or lower triangular matrices.
  3. Perform a variety of algebraic matrix operations, including multiplication of matrices, transposes, and traces.
  4. Calculate the inverse of a matrix using various methods, and perform application problems involving the inverse.
  5. Compute the determinant of square matrices and use the determinant to determine invertibility.
  6. Derive and apply algebraic properties of determinants.
  7. Perform vector operations on vectors from Euclidean Vector Spaces including vectors from R^n.
  8. Compute the equations of lines and planes and write these in their corresponding vector forms.
  9. Perform linear transformations in Euclidean vector spaces, including basic linear operatons, and determine the standard matrix of the linear transformation.
  10. Prove whether a given structure is a vector space and determine whether a given subset of a vector space is itself a vector space.
  11. Determine if a set of vectors spans a space, and if such a set is linearly dependent or independent.
  12. Determine if a set of functions is linearly independent using various techniques including calculating the determinant of the Wronskian.
  13. Solve for the basis and the dimension of a vector space.
  14. Determine the rank, the nullity, the column space and the row space of a matrix.
  15. Describe orthogonality between vectors in an abstract vecotr space by means of an inner product, and compute the inner product between vectors of this inner product space.
  16. Compute the QR-decomposition of a matrix using the Gram-Schmidt process.
  17. Perform changes of bases for a vector space, including computation of the transition matrix and determining an orthonormal basis for the space.
  18. Compute all the eigenvalues of a square matrix, including any complex eigenvalues and determine their corresponding eigenvectors..
  19. Determine if a square matrix is diagonalizable and compute the diagonalization of a matrix whose eigenvalues are easily calculated.
  20. Perform linear transformations among abstract general vector spaces, determining the rank, the nullity and the associated matrix of the transformation.