Hints and Answers for Assignment 2 Section 1.4: 3ce,4ce,5g,9,13 3. (c) Solve (3, 4, 1) = a1 (1, -2, 1) + a2 (-2, -1, 1), i.e. a1 - 2a2 = 3, -2a1 - a2 = 4 and a1 + a2 = 1 and find that there is no solution. Hence, the first vector is not in the span of the
Hints and Answers for Test I 1. (a) A vector space V over a eld F is a set on which operations of addition and scalar multiplication are dened so that x + y V if x, y V and kx V if x V and k F so that the following eight conditions hold. (i) x + y = y + x
Math 324: Assignment 7 Instructions. The following six exercises plus a written solution to the exercise you select to present in class are due on Monday, November 1. 0 1 1 2 5 by: 1. Evaluate the determinant of 1 6 4 3 (a) using the cofactor expansion al
Assignment 6: Hints and Answers. 1. (a) Put A in reduced row echelon form, the nonzero rows will form a basis of the row space of A. Hence cfw_(1, 0, -2, 1, 5), (0, 1, 1, -3, -7) is a basis for the row space of A. (b) (1, 0, -2, 1, 5) = 1(1, 0, -2, 1, 5)
Math 324, Test 1, October 13, 2004 Instructions. Do Part I and Part II as described below. No notes, books or calculators are allowed. Good Luck! Part I. Complete questions 1 and 2. 1. (30 pts) Dene the following concepts. (a) (6 pts) Vector Space (b) (3
Math 324, Autumn 2004, Assignment 4 (In-class) Exercise 1. Consider the transformation T : IR2 IR2 dened by T (x, y) = (x y, 2x + 3y) and the transformation U : IR2 IR3 dened by U (s, t) = (3s + t, 2s y, s). Then U T : IR2 R3 is a linear trasformation and
Math 324: Assignment 7, Hints and Answers Instructions. The following six exercises plus a written solution to the exercise you select to present in class are due on Monday, November 1. 0 1 1 2 5 by: 1. Evaluate the determinant of 1 6 4 3 (a) expanding al
Math 324, Test 2, November 10, 2004 Hints and Answers Instructions. Do 10 of the following 11 questions. The last three questions are take-home questions on which you may use MathCAD. 3 -1 -1 2 -1 . Find the eigenvalues of A. Find bases for 1. (a) Conside
Math 324: Assignment 6 Instructions. Exercises 1, 2, 3 are to be written and turned in on Monday, October 25. Exercises 2(a), 4, 5, 6 and 7 are for in-class presentation. Exercise 1. Consider the matrix 1 0 2 1 5 0 8 A = 3 1 5 1 2 0 5 9 Let the row-space
Math 324, Test 2, November 10, 2004 Instructions. Do 10 of the following 11 questions. The last three questions are take-home questions on which you may use MathCAD. 3 1 1 2 1 . Find the eigenvalues of A. Find bases for 1. (a) Consider the matrix A = 0 0