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LINEAR ALGEBRA

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Learning Outcomes

  • analyze the solution set of a system of linear equations.
  • express some algebraic concepts (such as binary operation, group, field).
  • do elemantary matrix operations.
  • express a system of linear equations in a matrix form.
  • do the elementary row operations for the matrices and systems of linear equations.
  • investigate the solition of a system using Gauss elimination.
  • apply Cramer's rule for solving a system of linear equations, if the determinant of the matrix of coefficients of the system is not zero.
  • generalize the concepts of a real (complex) vector space to an arbitrary finite-dimensional vector space.
  • definite a vector space and subspace of a vector space.
  • explain properties of R^n and subspaces of R^n.
  • determine whether a subset of a vector space is linear dependent.
  • describe the concept of a basis for a vector space.
  • investigate properties of vector spaces and subspaces using by linear transformations.
  • express linear transformation between vector spaces.
  • represent linear transformations by matrices.
  • explain what happens to representing matrices when the ordered basis is changed.
  • describe the concepts of eigenvalue, eigenvector and characteristc polynomial.
  • determine whether a linear transformation is diagonalizable or not.
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