Concept explainers
In each of Problems 10 through 14, determine whether the members of the given set of vectors are linearly independent. If they are linearly dependent, find a linear relation among them.
Want to see the full answer?
Check out a sample textbook solutionChapter A Solutions
Differential Equations: An Introduction to Modern Methods and Applications
Additional Math Textbook Solutions
Elementary Statistics (13th Edition)
Probability And Statistical Inference (10th Edition)
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
Pre-Algebra Student Edition
Graphical Approach To College Algebra
- For which values of t is each set linearly independent? a S={(t,0,0),(0,1,0),(0,0,1)} b S={(t,t,t),(t,1,0),(t,0,1)}arrow_forwardUse a software program or a graphing utility to write v as a linear combination of u1, u2, u3, u4, u5 and u6. Then verify your solution. v=(10,30,13,14,7,27) u1=(1,2,3,4,1,2) u2=(1,2,1,1,2,1) u3=(0,2,1,2,1,1) u4=(1,0,3,4,1,2) u5=(1,2,1,1,2,3) u6=(3,2,1,2,3,0)arrow_forwardIn each of the following linear functions, the independent variable represents time in minutes and the dependent variable represents distance in blocks. Find the representation that indicates a person was farthest from home after 10 minutes. a) b) y 1 2 2 3 3 4 c) y=2x– 8 d) Elizabeth starts at home and walks 6 blocks every 5 minutes. e) More than one of these could be the answer. 1,arrow_forward
- skip the first 3 thank youarrow_forwardGiven that v = (2,3, 4), vị = (1,0, 1), v2 = (0,–1,1), v3 = (-1,–1,1). %3D Express v as a linear combination of v1, v2, v3 .arrow_forwardQ.4. Let a, 3 and b (a) Determine if bis a linear combination of a,, a, and a,. (b) Determine if the vectors a,, a, and a, are linear independent.arrow_forward
- Is i,,3 a linearly independent set?d and ūs 2 2. 2. -3 3arrow_forwardWhich of the following sets of vectors are linearly independent? A. (4,8,-5), (-9, -4,-6), (-13, -12, -1) ● B. (1, -2, 4), (-8, 7, 0), (3, 6, 5) C. (-8, -2), (8,2) • D. (4, 8,-5), (-9, -4, -6), (-13, -1, -12 ), ( 4, 11, -13) E. (-3, 1, -2), (1, 7,-8) • F. (-1, 5), (9,-1) ● G. (-6, 1, 1, -2), (1, 7, -4,-9) H. (4, 6), (0,0)arrow_forwardA bird takes exactly two minutes to fly linearly from P(3,8,4) to Q(7,4,-3). Assuming that the bird maintains a constant speed, answer each of the following questions. What are the coordinates of the bird's position 45 seconds after leaving P? How many seconds after leaving P does the bird cross the xy-plane?arrow_forward
- Show that the set S= {(20, 34), (40, 68)} is linearly independent or not?arrow_forwardDetermine whether the following vectors are linearly dependent or independent and find a linear dependence relation between the vectors if one exists. -2 5 6. -4 5arrow_forward3. Show that the vectors v, = (0, 3, 1, -1); v, =(6, 0, 5, 1); v, = (4. -7, 1, 3) form a linearly dependent set in R*? 4. Express V1 in number 3 as linear combination of V2 and V3. %3Darrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningAlgebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell