Which of the following sets is a spanning set but not a basis for the vector space V={(a,b,c)∈R3∣a+b=0}? (a) {(1,1,0),(1,0,0),(0,1,0)}{(1,1,0),(1,0,0),(0,1,0)}. (b) {(1,−1,0),(1,−1,1)}{(1,−1,0),(1,−1,1)}. (c) {(1,−1,0),(0,0,1)}{(1,−1,0),(0,0,1)}. (d) {(−1,1,1),(1,−1,0),(0,0,2)}{(−1,1,1),(1,−1,0),(0,0,2)}. (e) {(−1,1,1),(1,0,−1),(0,1,0)}{(−1,1,1),(1,0,−1),(0,1,0)}.

Which of the following sets is a spanning set but not a basis for the vector space V={(a,b,c)∈R3∣a+b=0}? (a) {(1,1,0),(1,0,0),(0,1,0)}{(1,1,0),(1,0,0),(0,1,0)}. (b) {(1,−1,0),(1,−1,1)}{(1,−1,0),(1,−1,1)}. (c) {(1,−1,0),(0,0,1)}{(1,−1,0),(0,0,1)}. (d) {(−1,1,1),(1,−1,0),(0,0,2)}{(−1,1,1),(1,−1,0),(0,0,2)}. (e) {(−1,1,1),(1,0,−1),(0,1,0)}{(−1,1,1),(1,0,−1),(0,1,0)}.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Which of the following sets is a spanning set but not a basis for the vector space V={(a,b,c)∈R3∣a+b=0}?

(a) {(1,1,0),(1,0,0),(0,1,0)}{(1,1,0),(1,0,0),(0,1,0)}.

(b) {(1,−1,0),(1,−1,1)}{(1,−1,0),(1,−1,1)}.

(d) {(−1,1,1),(1,−1,0),(0,0,2)}{(−1,1,1),(1,−1,0),(0,0,2)}.

(e) {(−1,1,1),(1,0,−1),(0,1,0)}{(−1,1,1),(1,0,−1),(0,1,0)}.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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