Let y = - 12 -1 1 -8 2 , and V₂ = -5 1 . Find the distance from y to the subspace W of R4 spanned by v₁ and v₂, given that the closest point to y in W is y= 0 3 The distance is (Simplify your answer. Type an exact answer, using radicals as needed.) (...) -9 5 4 -5

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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LINEAR ALGEBRA QUESTION

Let
y=
−12
−1
1
−8
​,
v1=
1
−1
−1
2
​,
and
v2=
−5
1
0
3
.
Find the distance from y to the subspace W of
ℝ4
spanned by
v1
and
v2​,
given that the closest point to y in W is
y=
−9
5
4
−5
.
 
 
 

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Part 1
The distance is
enter your response here.
​(Simplify your answer. Type an exact​ answer, using radicals as​ needed.)
Let y =
12
1
1
- 8
1
1
- 1
2
and V₂ =
-5
3
Find the distance from y to the subspace W of R4 spanned by
1
The distance is
(Simplify your answer. Type an exact answer, using radicals as needed.)
...
and
V2,
given that the closest point to y in W is y =
9
5
4
- 5
Transcribed Image Text:Let y = 12 1 1 - 8 1 1 - 1 2 and V₂ = -5 3 Find the distance from y to the subspace W of R4 spanned by 1 The distance is (Simplify your answer. Type an exact answer, using radicals as needed.) ... and V2, given that the closest point to y in W is y = 9 5 4 - 5
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