Prep for GRE® Subject Math Exam-Module3: Linear Algebra

Explore linear systems by forming coefficient matrices, applying row operations, and row reducing to determine solutions, ranks, degrees of freedom, and the roles of particular and homogeneous solutions.

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.

This module presents a two-question quiz on matrices, showing quick determinant calculation via column additions and row subtractions, and applying trace concepts, with the determinant equal to 160.

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.

Explore eigenvalues and eigenvectors through the characteristic polynomial, eigen spaces, and the algebraic and geometric multiplicities. Practice computing determinants and eigenpairs with example matrices.

Complete the final quiz, featuring few questions with two and a half minutes each. Pace yourself, stop the video if needed, and know that answers appear in the next lecture.