MATH 251- PART ONE  THIS WILL BE THE MATERIAL ON THE FIRST EXAM (9/22)

1.1  systems of linear equations (overview)
augmented matrix
solution of linear systems via row operations
PROBLEMS: 6,7,8                                                     QUIZ 1: 9/1

1.2   row-echelon form and reduced row-echelon form
linear systems:  "leading variables" and "free variables"
Gauss and Gauss-Jordan elimination
homogeneous linear systems
PROBLEMS: 4,5, 6/7, 10/11, 12, 20, 21, 25, 26 QUIZ 1:9/1

1.3  matrix operations
left action on vectors and matrices
transpose matrices
PROBLEMS: 15,16,18,21,22                                   QUIZ  1:9/1

1.4 invertible matrices, properties of the inverse
matrix powers, polynomials of matrices
PROBLEMS: 4,7,8,15,16,18,19,22                           QUIZ 2:9/8

1.5  inverse via row reduction
PROBLEMS: 6,8,13
"elementary matrices": optional reading                QUIZ 2:9/8

1.6 invertibility and solution of systems
PROBLEMS: 11-14,16-19, 20, 21,22                    QUIZ 2:9/8

1.7 diagonal, triangular and symmetric matrices
PROBLEMS: 1,2,3, 24                                                  NO QUIZ

Sections 2.1 and 2.4 are "optional reading"

2.2: Determinants via row reduction
PROBLEMS: 3,4,5,12,13                                             QUIZ3:9/15

2.3 : Properties of determinants
PROBLEMS: 5,6,7,10,11,17                                       QUIZ 3:9/15

Chapter 3 will not be covered in class: "optional reading"

4.1  Euclidean n-space
PROBLEMS: 4,10,16,20,23,26                                  QUIZ 3:9/15

4.2    Linear transformations of Euclidean space
PROBLEMS: 9,11,13,17,18,20,21                               EXAM 1: 9/22

4.3   Properties of linear transformations
PROBLEMS: 3,4,13,14,18,19                                    EXAM 1:9/22