19 DEFIN Otherwise, they are called linearly independent. Let u = 0 i , and w= O 19.1 Describe span{u, v, w}. 19.2 Is {u, v, w} linearly independent? Why or why not? Let X = {u, v, w}. 19.3 Give a subset Y CX so that span Y = spanX and Y is linearly independent. 19.4 Give a subset Z CX so that span Z = span X and Z is linearly independent and Z #Y.
19 DEFIN Otherwise, they are called linearly independent. Let u = 0 i , and w= O 19.1 Describe span{u, v, w}. 19.2 Is {u, v, w} linearly independent? Why or why not? Let X = {u, v, w}. 19.3 Give a subset Y CX so that span Y = spanX and Y is linearly independent. 19.4 Give a subset Z CX so that span Z = span X and Z is linearly independent and Z #Y.
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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![19
DEFINITION
Linearly Dependent & Independent (Geometric)
We say the vectors V₁, V₂,...,Vn are linearly dependent if for at least one i,
V₁ E span{V₁, V2, Vi-1, Vi+1., Vn}.
Otherwise, they are called linearly independent.
[8]
19.1 Describe span{u, v, w}.
19.2 Is {u, v, w} linearly independent? Why or why not?
Let X = {u, v, w}.
Let u= 0, v =
H
0
and w = 1
19.3 Give a subset Y CX so that span Y = span X and Y is linearly independent.
19.4 Give a subset Z CX so that span Z = span X and Z is linearly independent and Z ‡ Y.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F28e7be30-eca9-4147-a850-5833b744a665%2F2413975c-521b-4ba9-b592-0661aa26e3e3%2Fj1q1wn_processed.png&w=3840&q=75)
Transcribed Image Text:19
DEFINITION
Linearly Dependent & Independent (Geometric)
We say the vectors V₁, V₂,...,Vn are linearly dependent if for at least one i,
V₁ E span{V₁, V2, Vi-1, Vi+1., Vn}.
Otherwise, they are called linearly independent.
[8]
19.1 Describe span{u, v, w}.
19.2 Is {u, v, w} linearly independent? Why or why not?
Let X = {u, v, w}.
Let u= 0, v =
H
0
and w = 1
19.3 Give a subset Y CX so that span Y = span X and Y is linearly independent.
19.4 Give a subset Z CX so that span Z = span X and Z is linearly independent and Z ‡ Y.
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