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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)}.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.3: Spanning Sets And Linear Independence
Problem 30EQ
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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)}.
Transcribed Image Text: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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