
Explore matrices as tables of numbers over real or complex fields, learn multiplication, transposes, inverses, determinants, and how rank governs invertibility and linear systems.
Explore matrix inverses, transposes, scalar and identity matrices, and row operations. Understand determinant nonzero implies invertibility and determinant multiplicativity, with minors and 2x2/3x3 tricks.
Explore vector spaces and subspaces, focusing on closure under addition and scalar multiplication, spans from generating sets, and examples like matrices, polynomials, kernel, and column spaces.
Explore bases and dimensions to transform a spanning set into a basis, using row reduction and rank to reveal subspaces, sums, and intersections in vector spaces.
More Practice Questions.
This course is a prep course for the GRE Subject exam in Mathematics. If you wish to apply for a grad program in math, statistics and such, this exam is required.
This is the third module and includes all the linear algebra material needed in order to excel in the exam. More importantly, the course teaches techniques for solving problems FAST (since in the exam you will have 2.5 min per question - very little time).
We will go over the following topics:
The course is designed to review all that is necessary to get you up to speed and get you solving real exam problems. Knowledge covered in the first module is assumed.
See the free intro lecture of the first module to get more details.
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