(1) Find the general solution of the equation sin x+ =2 cos.x (i1) The vector equations of two lines L, and L2 L:r =i+ 2j +1(2i+j+ 3k) L2:r = -j- 4k + µ(3i+ 2j + 5k) Find (a) The point of intersection of L,'and L2 (b) The vector parametric equation of the plane containing L1 and L2. 9. (i) Show that the equation xlnx+x-330 has a root between I and 2. Given that x= is a first approximate root, use one iteration of the Newton-Raphson procedure to obtain a second approximate root of this equation. (in) A class is made up of 5 boys and 8 girls. Find the number of ways in which a mixed delegation of 4 students can be chosen from the class if it must include at least 2 boys. WO statements p ond q are defined as foilows: p: the workers will go on strike. 4. there will be no salary. Write the following statements in correct English. (a) q = (b) q p (c) p

(1) Find the general solution of the equation sin x+ =2 cos.x (i1) The vector equations of two lines L, and L2 L:r =i+ 2j +1(2i+j+ 3k) L2:r = -j- 4k + µ(3i+ 2j + 5k) Find (a) The point of intersection of L,'and L2 (b) The vector parametric equation of the plane containing L1 and L2. 9. (i) Show that the equation xlnx+x-330 has a root between I and 2. Given that x= is a first approximate root, use one iteration of the Newton-Raphson procedure to obtain a second approximate root of this equation. (in) A class is made up of 5 boys and 8 girls. Find the number of ways in which a mixed delegation of 4 students can be chosen from the class if it must include at least 2 boys. WO statements p ond q are defined as foilows: p: the workers will go on strike. 4. there will be no salary. Write the following statements in correct English. (a) q = (b) q p (c) p

Name: 9iii 3x-2x-36=08 () Find the general solution of the equationsin r+TC3
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Description: 9iii 3x-2x-36=08 () Find the general solution of the equationsin r+TC32cos.x(i1) The vector equations of two lines L, and L2L:r =i+ 2j +1(2i+j+ 3k)L2:r = -j - 4k + (3i + 2j + 5k)Find(a) The point of intersection of L,'and L2(b) The vector parametric

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.4: The Singular Value Decomposition

Problem 49EQ

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(1) Choose two vectors v1, v2 in R 2 and another vector b also in R 2 . Find scalars x, y in R such that xv1 + yv2 = b (if this is not possible, pick other v1, v2, b vectors). Illustrate the vector equation you just solved by graphing the vectors v1, v2, b in the x − y-plane, and be sure to illustrate how b is obtained by adding a scalar of one vector to the other. (2) Repeat part 1 with vectors v1, v2, b in R 3 that give a consistent system. (3) Why is part 2 more difficult than part 1? Explain clearly using complete sentences.
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