San Jose State University Spring 2010 MATH129A Linear Algebra I, section 2 MW 13:30 14:45, MH 423 SYLLABUS
Instructor: Dr. Wasin So MacQuarrie Hall Room 418 408-924-5155 [email protected] www.math.sjsu.edu/~so Office hours: MW 10:00 11:00, M 15:00 17:00, a
Spring 2010 MATH129A Linear Algebra I, section 2 MW 13:30 14:45 TEST 1 Solution 1. (a) (b) (c) (d) (e) False False False False False
2. (a) List those are inconsistent: (b), (e) List those are having infinite solutions: (a), (d)
(b) The general solution
MATH 129A Linear Algebra I Project 1 Due in class on 2/17/2010 (W) There are many applications of systems of linear equations. Well over 75 percent of all mathematical problems encountered in scientific or industrial applications involve solving a linear
San Jose State University Spring 2010 MATH129A Linear Algebra I, section 2 CALENDAR
Date Jan 27 (W) Feb Feb Feb Feb Feb Feb 1 (M) 3 (W) 8 (M) 10 (W) 15 (M) 17 (W)
Topic introduction linear systems, reduction method vector equation, matrix equation solutio
Spring 2010 Answer of Section 2.8
2.8 #7 a. 3 b. infinitely many c. YES, because rref A p has non-pivot in the last column, hence p is a linear combination of columns of A. 2.8 #9 NO, because Ap = 0 2.8 #12 p = 3 and q = 4 2.8 #26 basis of Col(A) is
3 -
Spring 2010 Answer of HW5
2.3 #6 not invertible 2.3 #7 invertible 2.3 #15 No. Invertible matrix has linearly independent columns. 2.3 #20 If EF = I then E and F are inverses of each other, hence EF = I = F E. 2.3 #26 The existence of A2 means A is a squar
Spring 2010 Answer of Section 5.5
5.5 #1 the eigenvalues are 2 + i and 2 - i and the corresponding eigenvectors are and 5.5 #4 the eigenvalues are 4 + i and 4 - i and the corresponding eigenvectors are and 5.5 #5 the eigenvalues are 2 + 2i and 2 - 2i and
MATH 129A Linear Algebra I Project 1 solution
1. (a) x1 = the size of the field producing x2 = the size of the field producing (b) x1 + x2 = 5349 3 2 x1 + x2 = 3733 4 3 (c) x1 = 2004, 2. (a) There are 3 unknowns and they are x1 = number of measures in a b
Spring 2010 Answer of HW1
1.1 #13 The solution is (5, 3, -1). 1.1 #18 No. 1.1 #21 h can be any real number. 1.1 #25 The system is consistent if and only if k + 2g + h = 0. 1.1 #30
-1 R2 2
R2 , reverse: (-2)R2 R2
1.2 #1 rref: a, b ref: d none: c 1.2 #4
1
Spring 2010 Answer of Section 5.1
5.1 #2 YES, because det 5.1 #5 3 7 9 4 0 YES, because -4 -5 1 -3 = 0 and the eigenvalue is 0. 2 4 43 1 0 5.1 #13
0 a basis of EA (1) is 1
7 3 3 -1
- (-2)I2 = 0.
0
-1 a basis of EA (2) is 2
2
-1 a basis of EA (3) is 1
MATH129A, Linear Algebra I Project 2 Due in class on 4/5/2010 (M) Read the description of the spotted owl population at the beginning of Chapter 5 (page 301 302). To summarize, these owls have three distinct stages: juvenile (first year), subadult (second
Spring 2010 Answer of HW6
3.2 #8
Using replacing row operations only to obtain the ref: determinant is 0 3.2 #19 14 3.2 #29 Since det B = -2, det B 5 = (-2)5 = -32 3.2 #36
1 0 0 0
3 1 0 0
3 -4 2 -4 , hence the 0 1 0 0
Since 0 = det A4 = (det A)4 , det A
San Jose State University Spring 2010 MATH129A Linear Algebra I HOMEWORK "What we learn to do, we learn by doing." -Aristotle (384-322 BC)
Homework 1 due 2/8/2010 (M) Ex1.1 # 13, 18, 21, 25, 30, Ex1.3 # 5, 10, 13, 18, 25, Homework 2 due 2/17/2010 (W) Ex1.
San Jose State University Spring 2010 MATH129A Linear Algebra I PROJECT "What we learn to do, we learn by doing." -Aristotle (384-322 BC)
Project 1 due 2/17/2010 (W) Solving for unknowns in various situations Project 2 due 4/5/2010 (M) Making long term pr
REAL LINEAR ALGEBRA: PROBLEMS WITH SOLUTIONS
The problems listed below are intended as review problems to do before the
nal. They are organized in groups according to sections in my notes, but it is not
forbidden to use techniques from later sections (som