1. Say whether the following vectors are linearly independent and whether the vectors form a basisof R3. Support your answers with reasons.(a) {(1,2,3), (1,2,3)}.(b) {(1,2,3), (-1,2,3), (0, 0, 0)}.(c) {(2,-2, 1), (0, 2, 2), (2, 0, -1)}. (d) {(1, 1, 1), (1, −1, −1), (−1, 1, −1), (−1, −1,1)}.

Answered: Image /qna-images/answer/dade4736-80d6-46fa-9f6e-092e96bb2596.jpg

1. Say whether the following vectors are linearly independent and whether the vectors form a basis of R³. Support your answers with reasons. (a) {(1,2,3), (-1,2,3)}. (b) {(1,2,3), (-1,2,3), (0, 0, 0)}. (c) {(2,-2, 1), (0, 2, -2), (2,0,-1)}. (d) {(1, 1, 1), (1,-1,-1), (-1, 1, 1), (-1,-1,1)}.

1. Say whether the following vectors are linearly independent and whether the vectors form a basis of R³. Support your answers with reasons. (a) {(1,2,3), (-1,2,3)}. (b) {(1,2,3), (-1,2,3), (0, 0, 0)}. (c) {(2,-2, 1), (0, 2, -2), (2,0,-1)}. (d) {(1, 1, 1), (1,-1,-1), (-1, 1, 1), (-1,-1,1)}.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CM: Cumulative Review

Problem 12CM

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Question

1. Say whether the following vectors are linearly independent and whether the vectors form a basis
of R3. Support your answers with reasons.
(a) {(1,2,3), (1,2,3)}.
(b) {(1,2,3), (-1,2,3), (0, 0, 0)}.
(c) {(2,-2, 1), (0, 2, 2), (2, 0, -1)}. (d) {(1, 1, 1), (1, −1, −1), (−1, 1, −1), (−1, −1,1)}.

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