Maths 632 Brief notes on trigonometry January 31, 2008 An angle can be measured by placing it in a circle of radius one (a unit circle) and measuring the length of the arc it subtends:
Since a unit circle has perimeter 2 ; by this scheme a right angle rec
Maths 632 Brief notes on trigonometry January 31, 2008 An angle can be measured by placing it in a circle of radius one (a unit circle) and measuring the length of the arc it subtends:
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Since a unit circle has perimeter 2, by this scheme a right angle
Maths 632 Homework #5, Solutions March 27, 2008 section 2.5, # 5, section 2.6, #8 a,b, 9, 10 section 2.5, # 5 ! a. We are given the matrix A = ~ ~ basis vectors E1 and E2 :
p1 2 1 p 2 1 p 2 1 p 2 1 p 2 1 p 2 p1 2 1 p 2 1 p 2 1 p 2
: We can observe what th
Maths 632 Homework #3 February 21, 2008 Exercises 8, 9 in chapter 2.3 (p. 43) 8. We are asked to exhibit a linear transformation N (from R2 to R2 ) that is not the zero transformation (the transformation, denoted 0; which sends every vector to the zero ve
Maths 632 Homework #4 February 28, 2008 Chapter 2.4, exercises 7b, 8b, 9 Chapter 2.4, #7b. We are to nd all solutions to the homogeneous system 2x + y 4x 2y This system can be rewritten as a matrix equation 2 4 Since the determinant of the matrix 2 4 2 4
Maths 632 Homework #6 April 10, 2008 Section 3.1, exercise 3, p. 115, Section 3.3, exercises 9 and 10, p. 127 Section 3.1, exercise 3 ~ We know that the orthogonal projection PU X ~ ~ U is PU ~ ~ We know further that the projection QU ? X ~ ~ QU ? X ~ ~ X
Maths 632 Homework #7 April 17, 2008 HW #7: Section 3.4, exercises 2, 4, 6 0 134-135) (p. 1 0 1 a 0 0 x 2. The transformation given by the matrix @ 0 b 0 A acts on a vector @ y A as follows: 0 0 c z 0 10 1 0 1 a 0 0 x ax @ 0 b 0 A @ y A = @ by A 0 0 c z c