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LINEAR ALGEBRA 1

Module code: MT113SC
Credits: 5
Semester: 1 and 2
Department: MATHEMATICS AND STATISTICS
International:

	Overview
	Module Objective: To introduce students to linear equations, determinants, vectors, complex numbers and matrices. Solving systems of linear equations by Gaussian elimination; determinants via row operations; coordinate geometry in 1,2 and 3 dimensions; position vectors and displacement vectors; vector arithmetic, norm, distance, dot product and angle, orthogonal projection, triangle and Cauchy-Schwartz inequalities, cross product in 3-dimensions; describe lines and planes using linear equations; complex numbers and the plane; matrix algebra; determinants as areas and volumes, determinant of a product; inverses and eigenvalues of 2x2 matrices and linear equations; other topics such as roots of unity, geometric problems, quadratic forms, linear maps via 2x2 matrices.

Overview

Module Objective: To introduce students to linear equations, determinants, vectors, complex numbers and matrices.

Solving systems of linear equations by Gaussian elimination; determinants via row operations; coordinate geometry in 1,2 and 3 dimensions; position vectors and displacement vectors; vector arithmetic, norm, distance, dot product and angle, orthogonal projection, triangle and Cauchy-Schwartz inequalities, cross product in 3-dimensions; describe lines and planes using linear equations; complex numbers and the plane; matrix algebra; determinants as areas and volumes, determinant of a product; inverses and eigenvalues of 2x2 matrices and linear equations; other topics such as roots of unity, geometric problems, quadratic forms, linear maps via 2x2 matrices.

	Learning Outcomes
	On successful completion of the module, students should be able to: Solve linear equations using Gaussian Elimination. Compute the determinant of an n x n matrix. Understand and draw 2 and 3 dimensional diagrams. Find dot products, norms, projections and angles. Write down the equations for lines and planes in space. Coordinatize lines and planes in space. Perform operations with matrices. Find the inverse and eigenvalues of a 2x2 matrix. Use the methods from the course to solve problems. State definitions and theorems covered in the course.

Learning Outcomes

Teaching & Learning methods

Assessment

	Autumn Supplementals/Resits
	Continuous assessment mark is carried forward to the Autumn. University scheduled written examination (Autumn): 90 minutes

Timetable

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Courses / Module

LINEAR ALGEBRA 1

Semester 1

Semester 2