Systems of Linear Equations
Linear Algebra and its Applications David C. Lay
- Winter 2008 p. 1/1
Method
A linear equation in the variables x1 , x2 , . . . , xn is an equation of the form a1 x1 + a2 x2 + . . . + an xn = b where the value b and coefficient
MATH 2008/09B WINTER 2005 AN OLD FINAL EXAM
1. Determine whether the lines: r1 = (2, -1, 0) + t(1, 2, -3) and r2 = (-1, 1, 2) + s(-2, 1, 1) are parallel, intersecting, or skew. If they intersect, find the point of intersection. 2. (a) Find a vector equati
MATH 2107B Names:
Tutorial 1
5:30-6:30pm
January, 2008
1
1 mark per multiple choice, 2 marks per long answer. The tutorial is out of 10 marks. Please work in groups.
Multiple Choice
1. For what values of h is the matrix below the augemented matrix of a co
MATH 2107 B
Complex Numbers
Exercises
Winter 2008
1
1. Write the following in polar coordinate representation. (a) z = (b) z =
3 2 1 2
+ -
i 2 i 2
(d) z = i
(c) z = - 1 + i 2 (e) z = -4
3 2
(f) z = -i (g) z = - 3 - i 2. Write z 2 , z 12 , z 100 , z n in
MATH 2107 B
Suggested Homework Problems
Winter 2008
1
The exercises suggested below are a MINIMUM. Review: Do the Practice Problems in each of the Sections plus, Chapter 1: 1.1 #1 - 29, 31, 33 (odd) 1.2, #1, 3, 9, 11, 13, 17, 21 1.3. #5 - 25 (odd) 1.4. #1
MATH 2107 B
Complex Numbers
Exercises
Winter 2008
1
1. Let c1 = 3 + 4i, c2 = 1 - 2i, and c3 = -1 + i. Compute each of the following and simplify as much as possible. (a) c1 + c2 (b) c3 - c1 (c) c1 c2 (d) c2 c3 (e) 4c2 + c2 (f) (-i)c2 (g) 3c1 = ic2 (h) c1
Linear Algebra II
MATH 2107B, Winter 2008
Instructor: Lani Haque Office: Herzberg Physics 3390 Tel: (613) 520-2600 (Ext. 2142) E-mail: lhaque at math dot carleton dot ca Textbook: David C. Lay, Linear Algebra and its Applications, Addison-Wesley, 3rd edit
Section 4.4 Coordinate Systems
Linear Algebra and its Applications David C. Lay
- Winter 2008 p. 1/
Given a basis B = cfw_b1 , . . . , bn for a vector space V . For each x V there exists a unique set of scalars c1 , c2 , . . . , cn such that x = c1 b1 +
Section 4.3 Linearly independent sets; bases
Linear Algebra and its Applications David C. Lay
- Winter 2008 p. 1/1
Let's start with a vector space V and an ordered subset cfw_v1 , , vp V . The ideas are similar to those for Rn . cfw_v1 , , vp V is said
Section 4.2 Null Spaces, Column Spaces and Linear Transformations
Linear Algebra and its Applications David C. Lay
- Winter 2008 p. 1/1
The technical/mechanics of this section are familar to us. The terminology is new. Let's begin! The nullspace of a matr
Section 4.1 Vector Spaces and Subspaces
Linear Algebra and its Applications David C. Lay
- Winter 2008 p. 1/1
Vector Spaces and Subspaces
Recall in 1.3 we looked at vector equations where our vectors were from R2 , R3 , R4 , . . . , Rn , n 1. R2 , R3 , Rn