MTH 261

 

INTRODUCTION  TO LINEAR ALGEBRA

 

Professor:  Serge Preston

 

Office:  Neuberger Hall M316, PSU

 

Phone:  725-3637

 

Office hours:   Mon., Wed.  11:30-12:30 AM, or by appointment

 

Text: Poole, D., Linear Algebra, A Modern Introduction, Third Ed. We will cover  Chapters 1-4 with some omissions.

 

Your grade will be based on:

 

               * Final Examination (in class, open book): End of the Term. No

                        grade without Final.

                 *      Midterm exam. (in class, open book): Middle of the Term. No

                        grade without Midterm.

               *     Almost class you will have a quiz (open book). 

                  * Your class participation: comments, questions, discussion,

                        presentation are VERY appreciated and will serve as one of

                        the grading tools.

                   *Homework can be done in small groups.  Problems similar to the HW

                   problems will be given at quizzes. 

         Homework will not be used  for grades.

 

     GRADE: Quizes- 40%, Midterm – 20%, Final – 40%.

 

             I strongly recommend you to come to my office to discuss your questions and problems.

 

      A happy New Term!

 

 

 

HOMEWORK

 

 

Sec.1.1

2.a,c ; 3b,d; 11;12;17;21;//// 27;33;37;45

17-20
Sec.1.2 1;3;9; 15; 25;31; 37; 43; 51; 

24-26,40-45,55-70
Sec.1.3

1;5;7;11;18-19; 27; 37;43
distance, points of intersections

Sec.2.1 

15; 21;29;39a;41;43 

 

Sec.2.2 

1;5;9;17;27;31;35;41;45;49 

25-34,40-44,48-50 

 Sec.2.3

3,5,9,11,17,25,29, 43a,b 

1-6,8-12,18-21,22-31,42-48, 





Sec.3.1

5,7,15,21,31,35,

 

Sec.3.2 

5,15,23,41 

13-16,38-48 

Sec.3.3 

5,10,13a),33 

3-10,35,38 
Sec.3.5
                   11,15,17,35,45,47,57
57-66
Sec 3.6
 1,9,15,17,23,31,41*, 45*


Sec.4.1
 1,5,9,11,15,17,27,29,


Sec.4.2
 3,11,12,15,29,33,45,57,


sec.4.3
 7,11,17,19b,21,23,
All










 


Topics/notions:


Chapter I.

Vectors, Dot product, length, angle, linear combinations.
Triangle inequality, Cauchy-Schwatz inequality, distanse between points, angles, orthogonality, projections
equations for lines, planes, points and lines of intersections.


Chapter II.

Systems of linear equations, solutions, homogeneous equations. Augmented matrix of a linear system.
Row echelon form of a matrix, elementary row operations.
Rank of matrix.
Reduction to row echelon form and solving of linear systems - 3 cases - no sol, one sol, continuum sol.

Linearly independent  (dependent) sets of vectors.
basis in R^n, decomposition of a vector bu a basis.
linear span of a set of vectors.
Subspaces, dimension.

Chapter III

Operations with matrices.
Matrices: transposed, symmetric, diagonal, triangular, skew-symmetric.

Inverse matrix ,elementary matrices and row operations. Theorem 3.12.
Linear tyransformations, their matrices. composition of linear transfoprmations, inverse transformations.

Null space of matrix, Rank of linear transformation.  Basis, dimension.


Chapter IV.

Eigenvalues, eigenvectors, characteristic equations.
Determinant, minor, cofactor, Laplace formulas for Det.
Triangular matrices, Thm 4.3, determinants of inverse, product, transposed.