How to study Algebra & Geometry — Semester II, Pokhara University BECE
What it covers
Linear algebra and analytic geometry for engineers: matrices and determinants, systems of linear equations, vector spaces, eigenvalues and eigenvectors, vectors, and the geometry of lines, planes and conic sections.
Topics worth extra time
- Matrices and determinants: rank, inverse and their properties
- Systems of linear equations: consistency and solution methods
- Vector spaces, linear independence, basis and dimension
- Eigenvalues and eigenvectors, and the Cayley–Hamilton theorem
- Analytic geometry: lines, planes, spheres and conic sections in three dimensions
How to study it
Linear algebra rewards understanding the definitions exactly, since most proofs follow directly from them. Practise row reduction until it is quick and accurate, because it underlies rank, inverses and solving systems. For geometry, sketch each surface or line before calculating.
In the exam
Arithmetic slips are the usual cause of lost marks in matrix questions, so check your working (for example, multiply back to verify an inverse). Write proofs in clear steps, quoting the property you use at each step.