PLEASE, I NEED A DETAILED STEP-STEP PROCESS WITH EX- PLANATIONS TO THIS QUESTION. (I have no prior knowledge in Algebra, so be simple as much as possible for me.) THANK YOU Let E be any vector space over K and {u;}iel any family of vectors in E (the family could be in infinite). Let ug, ut be any two vectors in the family (s t) and let a E K be arbitrary. Show that Span(u, u}ie1) Span(ugau{u;}iel1) where I1 I\{s}. This means that one can add any multiple of any vector to any other vector in the family, and the spanning space does not change. Hence deduce that Span(w, u}ie) Span(ua, u}ie) Span(w, fu4}ieI) where w is any finite combination of the vectors in the family that contains us with a nonzero coefficient. (Here matrix and how the row space changes.) one should make connection to row operations of a

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 45E
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I have no strong background in Algebra, so be simple and basic as much as possible for me to grasp each step that you will be provided. I will also rate your answer very high. Thank you so much.

PLEASE, I NEED A DETAILED STEP-STEP PROCESS WITH EX-
PLANATIONS TO THIS QUESTION.
(I have no prior knowledge in Algebra, so be simple as much as possible
for me.) THANK YOU
Let E be any vector space over K and {u;}iel any family of vectors in E (the
family could be in infinite). Let ug, ut be any two vectors in the family (s t) and
let a E K be arbitrary. Show that
Span(u, u}ie1)
Span(ugau{u;}iel1)
where I1 I\{s}. This means that one can add any multiple of any vector to any
other vector in the family, and the spanning space does not change. Hence deduce
that
Span(w, u}ie)
Span(ua, u}ie) Span(w, fu4}ieI)
where w is any finite combination of the vectors in the family that contains us with
a nonzero coefficient. (Here
matrix and how the row space changes.)
one should make connection to row operations of a
Transcribed Image Text:PLEASE, I NEED A DETAILED STEP-STEP PROCESS WITH EX- PLANATIONS TO THIS QUESTION. (I have no prior knowledge in Algebra, so be simple as much as possible for me.) THANK YOU Let E be any vector space over K and {u;}iel any family of vectors in E (the family could be in infinite). Let ug, ut be any two vectors in the family (s t) and let a E K be arbitrary. Show that Span(u, u}ie1) Span(ugau{u;}iel1) where I1 I\{s}. This means that one can add any multiple of any vector to any other vector in the family, and the spanning space does not change. Hence deduce that Span(w, u}ie) Span(ua, u}ie) Span(w, fu4}ieI) where w is any finite combination of the vectors in the family that contains us with a nonzero coefficient. (Here matrix and how the row space changes.) one should make connection to row operations of a
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