ит 3 (1,-1,1) из — (2, 1, —2) из — (10, 2, —6). %3D Is the set {u1, u2, U3} linearly dependent or linearly independent?
ит 3 (1,-1,1) из — (2, 1, —2) из — (10, 2, —6). %3D Is the set {u1, u2, U3} linearly dependent or linearly independent?
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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![**§5.4, Exercise 3.**
Let
\[ u_1 = (1, -1, 1) \quad u_2 = (2, 1, -2) \quad u_3 = (10, 2, -6) \]
Is the set \(\{u_1, u_2, u_3\}\) linearly dependent or linearly independent?
---
This exercise involves determining the linear dependency of a set of vectors in \(\mathbb{R}^3\). Three vectors \(u_1\), \(u_2\), and \(u_3\) are given, and the task is to check whether these vectors are linearly dependent or independent. Linear dependency implies that one of the vectors can be written as a linear combination of the others, whereas independence means none of the vectors can be expressed in such a manner. Analyzing the coefficients or using methods like matrix row reduction can solve this problem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9fd5ba49-7d01-4178-9fd2-555b265ff7cd%2F35746df4-76b8-4136-a2fc-4e7f75814ee8%2Fn8ae0r_processed.png&w=3840&q=75)
Transcribed Image Text:**§5.4, Exercise 3.**
Let
\[ u_1 = (1, -1, 1) \quad u_2 = (2, 1, -2) \quad u_3 = (10, 2, -6) \]
Is the set \(\{u_1, u_2, u_3\}\) linearly dependent or linearly independent?
---
This exercise involves determining the linear dependency of a set of vectors in \(\mathbb{R}^3\). Three vectors \(u_1\), \(u_2\), and \(u_3\) are given, and the task is to check whether these vectors are linearly dependent or independent. Linear dependency implies that one of the vectors can be written as a linear combination of the others, whereas independence means none of the vectors can be expressed in such a manner. Analyzing the coefficients or using methods like matrix row reduction can solve this problem.
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