# Singapore University of Social Sciences

## Linear Algebra (MTH207)

### Synopsis

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

### Topics

• 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.