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6. Determine whether the set of all linear combinations of the following set of vector in R³ is a line or a plane or all of R³. Justify, your answer. (a) {(-2,5,-3), (6, -15,9), (-10, 25, -15)} (b) {(1,2,0), (1, 1, 1), (4,5,3)} (c) {(0,0,3), (0, 1, 2), (1, 1,0)}

6. Determine whether the set of all linear combinations of the following set of vector in R³ is a line or a plane or all of R³. Justify, your answer. (a) {(-2,5,-3), (6, -15,9), (-10, 25, -15)} (b) {(1,2,0), (1, 1, 1), (4,5,3)} (c) {(0,0,3), (0, 1, 2), (1, 1,0)}

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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6. Determine whether the set of all linear combinations of the following set of vector in R³ is a line or a plane or all of R³. Justify, your answer. (a) {(-2,5,-3), (6, -15,9), (-10, 25, -15)} (b) {(1,2,0), (1, 1, 1), (4,5,3)} (c) {(0,0,3), (0, 1, 2), (1, 1,0)}
Transcribed Image Text:6. Determine whether the set of all linear combinations of the following set of vector in R³ is a line or a plane or all of R³. Justify, your answer. (a) {(-2,5,-3), (6, -15,9), (-10, 25, -15)} (b) {(1,2,0), (1, 1, 1), (4,5,3)} (c) {(0,0,3), (0, 1, 2), (1, 1,0)}
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