Singapore University of Social Sciences

Linear Algebra

Linear Algebra (MTH207)


MTH207 introduces essentials of linear algebra and shows the relationships between them. As linear algebra uses linear transformations to study systems of linear equations, students should have a sound knowledge of mathematics, as developed in Further Discrete Mathematics and Further Calculus and Algebra.

Level: 2
Credit Units: 5
Presentation Pattern: Every July


  • Evaluate determinants by row or column expansions.
  • List and use properties of determinants.
  • Define systems of linear equations and the nature of their solutions.
  • Solve linear systems by Gaussian Elimination and Gauss-Jordon methods.
  • Define and list properties of Linear Transformations.
  • Perform matrix algebra.
  • Define general vector space V.
  • Define basis and dimension of V.
  • Find row space, Column space and Null space of an m x n matrix.
  • Find rank and nullity of a matrix.
  • Orthogonality.
  • Eigenvalues and Eigenvectors.

Learning Outcome

  • Show how to prove a mathematical statement in linear algebra.
  • Calculate the determinant, eigenvalues and/or eigenvectors of a square matrix.
  • Determine whether given subsets are linearly independent or are spanning sets of given subspaces.
  • Compute row echelon form, row space, column space, null space or rank of a given matrix.
  • Apply the Gram-Schmidt process to obtain an orthonormal basis for a given inner product space.
  • Solve system of linear equations.
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