psLinAlgebra1Ans

psLinAlgebra1Ans - Fall 2007 ARE211 Problem Set #06- Answer...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Fall 2007 ARE211 Problem Set #06- Answer key First Lin Algebra Problem Set (1) Simon & Blume question 10.5 (page 208). Ans: Let u = (1,2), v = (0,1), w = (1,-3), x = (1,2,0) and z = (0,1,1) (i) u + v = (1,2)+(0,1) = (1,3). (ii) -4* w = -4*(1,-3) = (-4,12). (iii) u + z is not defined as u is an (1x2) vector and z is an (1x3) vector. (iv) 3* z = 3*(0,1,1) = (0,3,3). (v) 2* v = 2*(0,1) = (0,2). (vi) u +2* v = (1,2)+2*(0,1) = (1,4). (vii) u- v = (1,2)-(0,1) = (1,1). (viii) 3* x + z = 3*(1,2,0)+(0,1,1) = (3,7,1). (ix) -2* x = -2*(1,2,0) = (-2,-4,0). (x) w + 2* x is not defined as w is an (1x2) vector and x is an (1x3) vector 2 (2) Simon & Blume question 10.10 (page 220) Ans: The vectors for part a,b,d,e, and g are displayed in figure 1. The vectors for part c and f are diplayed in figure 2. Figure 1. The vectors for part a,b,d,e, and g 1 2 3 4-1-2-3 1 2 3 4-1-2-3 x1-axis x2-axis part (a) part (b) part (d) part (e) part (g) a) || (3 , 4) || = 3 2 + 4 2 = 9 + 16 = 25 = 5 b) || (0 ,- 3) || = radicalbig 2 + (- 3) 2 = 0 + 9 = 9 = 3 c) || (1 , 1 , 1) || = 1 2 + 1 2 + 1 2 = 1 + 1 + 1 = 3 d) || (3 , 3) || = 3 2 + 3 2 = 9 + 9 = 2 * 9 = 3 * 2 e) || (- 1 ,- 1) || = radicalbig (- 1) 2 + (- 1) 2 = 1 + 1 = 2 f) || (1 , 2 , 3) || = 1 2 + 2 2 + 3 2 = 1 + 4 + 9 = 14 g) || (2 , 0) || = 2 2 + 0 2 = 4 + 0 = 4 = 2 h) || (1 , 2 , 3 , 4) || = 1 2 + 2 2 + 3 2 + 4 2 = 1 + 4 + 9 + 16 = 30 i) || (3 , , , 0) || = 3 2 + 0 2 + 0 2 + 0 2 = 9 + 0 + 0 + 0 = 9 = 3 3 (3) Suppose you know that the angle between two vectors is as given below. What do you know about the sign of the inner product of the two vectors? a) 180 b) 53 c) 320 d) 90 Ans: Recall that the sign of the inner product of two vectors v 1 and v 2 is given by the sign of the cosinus of the angle between them. a) cos (180) =- 1 The sign of the inner product is negative. Figure 2. The vectors for part 2c and 2f 1 2 3 1 2 3 1 2 3 x1-axis part (c) part (f) x2-axis x3-axis 4 b) cos (53) > The sign of the inner product is positive. c) cos (320) > The sign of the inner product is positive. d) cos (90) = 0 The sign of the inner product is zero as the vectors are perpendicular....
View Full Document

Page1 / 6

psLinAlgebra1Ans - Fall 2007 ARE211 Problem Set #06- Answer...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online