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Which of the following are spanning sets for R³? Justify your answer. (a) {(1, 0, 0), (0, 1, 0), (0, 0, 1)} (b) {(1, 0, 0), (0, 2, 2), (1, 1, 1)} (c) {(1, 0, 0), (0, 1, 0), (0, 0, 1), (1, 1, 1)} (d) {(1, 0, 0), (0, 1, 1), (1, 0, 1)} (e) {(1, 1, 1), (0, 0, 1)}

Which of the following are spanning sets for R³? Justify your answer. (a) {(1, 0, 0), (0, 1, 0), (0, 0, 1)} (b) {(1, 0, 0), (0, 2, 2), (1, 1, 1)} (c) {(1, 0, 0), (0, 1, 0), (0, 0, 1), (1, 1, 1)} (d) {(1, 0, 0), (0, 1, 1), (1, 0, 1)} (e) {(1, 1, 1), (0, 0, 1)}

Advanced Engineering Mathematics
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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Which of the following are spanning sets for R³? Justify your answer. (a) {(1, 0, 0), (0, 1, 0), (0, 0, 1)} (b) {(1, 0, 0), (0, 2, 2), (1, 1, 1)} (c) {(1, 0, 0), (0, 1, 0), (0, 0, 1), (1, 1, 1)} (d) {(1, 0, 0), (0, 1, 1), (1, 0, 1)} (e) {(1, 1, 1), (0, 0, 1)}
Transcribed Image Text:Which of the following are spanning sets for R³? Justify your answer. (a) {(1, 0, 0), (0, 1, 0), (0, 0, 1)} (b) {(1, 0, 0), (0, 2, 2), (1, 1, 1)} (c) {(1, 0, 0), (0, 1, 0), (0, 0, 1), (1, 1, 1)} (d) {(1, 0, 0), (0, 1, 1), (1, 0, 1)} (e) {(1, 1, 1), (0, 0, 1)}
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