Which of the following subsets in the vector space R^3 is linearly independent? (a) {(0,0,0), (1,0,1), (1,0,0)}. (b) {(0,0,1), (0,1,0), (0,1,1)}. (c) {(1,0,0), (0,1,0), (1,0,1), (1,1,1)}. (d) {(1,-1,0), (-1,1,0)}. (e) {(1,0,1), (0,-1,1)}.

Which of the following subsets in the vector space R^3 is linearly independent? (a) {(0,0,0), (1,0,1), (1,0,0)}. (b) {(0,0,1), (0,1,0), (0,1,1)}. (c) {(1,0,0), (0,1,0), (1,0,1), (1,1,1)}. (d) {(1,-1,0), (-1,1,0)}. (e) {(1,0,1), (0,-1,1)}.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.5: Basis And Dimension

Problem 65E: Find a basis for the vector space of all 33 diagonal matrices. What is the dimension of this vector...

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Question

Which of the following subsets in the vector space R^3 is linearly independent?

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

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

(d) {(1,-1,0), (-1,1,0)}.

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

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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