Let ū== = [1,2,0]T and 7 = = [1,0, 3]T. (a) (2 points) What is span{u, u}? (You can describe this algebraically, geometrically, or in your own words; but be precise!) span {u, v'} Spon { [] [] [] * span 2 (64)-(6)] -2 3 03 both they are Linearly inslependent independent in 7R3, there fore both vector form or plane in Ph ³. (b) (3 points) Show that the vector w = [8, 10,9] is in span{ū,v}. GU + G V =. W 1 78 705 [][ 2 16 39 ][ :) 60 o there is no pivol column in in therefore the w is in the pan { 0,0} (c) (3 points) Is the set {u,, w} linearly independent or linearly dependent? Make sure to justify your answer. ue can as from per (6) the w we could get linear dependant from the {v} الله
Let ū== = [1,2,0]T and 7 = = [1,0, 3]T. (a) (2 points) What is span{u, u}? (You can describe this algebraically, geometrically, or in your own words; but be precise!) span {u, v'} Spon { [] [] [] * span 2 (64)-(6)] -2 3 03 both they are Linearly inslependent independent in 7R3, there fore both vector form or plane in Ph ³. (b) (3 points) Show that the vector w = [8, 10,9] is in span{ū,v}. GU + G V =. W 1 78 705 [][ 2 16 39 ][ :) 60 o there is no pivol column in in therefore the w is in the pan { 0,0} (c) (3 points) Is the set {u,, w} linearly independent or linearly dependent? Make sure to justify your answer. ue can as from per (6) the w we could get linear dependant from the {v} الله
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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Question
![7. Let = [1,2,0]T and = = [1,0,3]¹.
(a) (2 points) What is span{u, }? (You can describe this algebraically, geometrically, or in your
own words; but be precise!)
sparu, √5 - pe { [!] [; }} WA
}
span
=)
44
-2
6 3
3
both
they
are
linearly independent in R3, there fore both vector
in
form
plane
PR ³.
01
(b) (3 points) Show that the vector w = [8, 10,9] is in span{ū,7}.
C U T Q V =. W
1 8
05
0
U-E-CAD-MA
10
2 16
=)
3
3
9
бо
there is no
therefore the w is in the yon { U₁U'}
piral column in
pan
(c) (3 points) Is the set {u,, w} linearly independent or linearly dependent? Make sure to justify
your answer.
from par (6)
as
he can
we could
the
get
at
Ilnear dependent
from the {0,²}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2e6b1be0-596d-4af1-a341-a1c152f1c814%2Fe8b00972-1fd2-4243-963c-46d4d7dbb159%2F3x8l8lc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:7. Let = [1,2,0]T and = = [1,0,3]¹.
(a) (2 points) What is span{u, }? (You can describe this algebraically, geometrically, or in your
own words; but be precise!)
sparu, √5 - pe { [!] [; }} WA
}
span
=)
44
-2
6 3
3
both
they
are
linearly independent in R3, there fore both vector
in
form
plane
PR ³.
01
(b) (3 points) Show that the vector w = [8, 10,9] is in span{ū,7}.
C U T Q V =. W
1 8
05
0
U-E-CAD-MA
10
2 16
=)
3
3
9
бо
there is no
therefore the w is in the yon { U₁U'}
piral column in
pan
(c) (3 points) Is the set {u,, w} linearly independent or linearly dependent? Make sure to justify
your answer.
from par (6)
as
he can
we could
the
get
at
Ilnear dependent
from the {0,²}
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