Week

Topics

Course Outcomes

1

Introduction to Systems of Linear Equations, Gaussian Elimination

IIIIII

2

Matrices and Matrix Operations, Inverses, Algebraic Properties of Matrices

IIIIIIIV

3

Elementary Matrices and a Method for Finding A1, More on Linear Systems and Invertible Matrices, Diagonal, Triangular, and Symmetric Matrices

IIIIIIVV

4

Determinants by Cofactor Expansion, Evaluating Determinants by Row Reduction

VI

5

Properties of Determinants, Cramer’s Rule

VIVII

6

Vectors in 2Space, 3Space, nSpace, Norm, Dot Product, and Distance in Rn, Orthogonality, The Geometry of Linear Systems, Cross Product

IIIIIVIII

7

Real Vector Spaces, Subspaces, Linear Independence, Coordinates and Basis, Dimension

IIIIII

8

MIDTERM


9

Change of Basis, Row Space, Column Space, and Null Space, Rank, Nullity

VI

10

Eigenvalues and Eigenvectors, Diagonalization

IIIIIIV

11

Orthogonal Matrices, Orthogonal Diagonalization, Quadratic Forms, Optimization Using Qudaratic Forms

II

12

Hermitian, Unitary, and Normal Matrices, Linear Transformations, Isomorphism

IIIVV

13

Compositions and Inverse Transformations

IIIVVIII

14

Matrices for General Linear Transformations

IIIVX
