Find the best approximation to z by vectors of the form C₁ V₁ + C₂ V₂. 3 -5 -2 HH V₁ = V₂ 0 Z= The best approximation to z is 972 9 1 1 3 (Simplify your answer.) Try again. Let W be a subspace of Rn, let y be any vector in Rn, and let y be the orthogonal projection of y onto W. Then, y is the closest point in W to y in the sense that ly-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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LINEAR ALGEBRA
Find the best approximation to
z
by vectors of the form
c1v1+c2v2.
 
z=
  2  
−5
4
2
​,
v1=
  3  
−2
0
1
​,
v2=
  1  
1
3
−1
 
 
 

Question content area bottom

Part 1
The best approximation to
z
is
Start 2 By 1 Table 1st Row 1st Column nine sevenths 2nd Row 1st Column seven twelfths EndTable
  97  
712
.
​(Simplify your​ answer.)
Find the best approximation to z by vectors of the form C₁ V₁ + C₂ V₂.
2
3
5
HHH
, V₁
4
2
1
Z=
The best approximation to z is
ON
7
12
1
1
3
1
(Simplify your answer.)
> Try again.
Let W be a subspace of Rn, let y be any vector in Rh, and let y be the orthogonal
projection of y onto W. Then, y is the closest point in W to y in the sense that
ly-ŷ|| < |y - v for all v distinct from y.
OK
X
Transcribed Image Text:Find the best approximation to z by vectors of the form C₁ V₁ + C₂ V₂. 2 3 5 HHH , V₁ 4 2 1 Z= The best approximation to z is ON 7 12 1 1 3 1 (Simplify your answer.) > Try again. Let W be a subspace of Rn, let y be any vector in Rh, and let y be the orthogonal projection of y onto W. Then, y is the closest point in W to y in the sense that ly-ŷ|| < |y - v for all v distinct from y. OK X
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