Determine whether the members of the given set of vectors are linearly independent. If they are linearly dependent, find a linear relation among them. 1 ( 1 x(1) x(2). x(3) 6 2 1 The vectors are linearly independent. X = Choose one Choose one x(1) + 6x(3) 6x(1) 6x4) + x(2) + 6x(3) 6x) +x 2) — 6х(3) %3| бх1) + 6x2) — х (3) — 0 ||

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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Linear Independence of vectors

Determine whether the members of the given set of vectors are
linearly independent. If they are linearly dependent, find a linear
relation among them.
"- () --()-()
1
1
x(1)
x(2)
x(3)
2
6.
1
The vectors are linearly independent.
X = |Choose one
Choose one
x(1) + 6x(3) :
6x0) + х?) + 6х(3)
+x(2)
+ 6x3) = 0
6x(1)
+x(2) — 6х(3)
— 0
6x1) + 6x(2) – x(3)
= 0
-
Transcribed Image Text:Determine whether the members of the given set of vectors are linearly independent. If they are linearly dependent, find a linear relation among them. "- () --()-() 1 1 x(1) x(2) x(3) 2 6. 1 The vectors are linearly independent. X = |Choose one Choose one x(1) + 6x(3) : 6x0) + х?) + 6х(3) +x(2) + 6x3) = 0 6x(1) +x(2) — 6х(3) — 0 6x1) + 6x(2) – x(3) = 0 -
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