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4 5 8 U₂ -2, and u3 = 1 -0 -4 1 R³ that is orthogonal to u₁ and ₂. Let u₁ = The nonzero vector v = . Note that u₁ and u₂ are orthogonal. It can be shown that u3 is not in the subspace W spanned by u₁ and u₂. Use this to construct a nonzero vector v in is orthogonal to u₁ and u₂.

4 5 8 U₂ -2, and u3 = 1 -0 -4 1 R³ that is orthogonal to u₁ and ₂. Let u₁ = The nonzero vector v = . Note that u₁ and u₂ are orthogonal. It can be shown that u3 is not in the subspace W spanned by u₁ and u₂. Use this to construct a nonzero vector v in is orthogonal to u₁ and u₂.

Advanced Engineering Mathematics
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

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Part 1
Let
u1=
  4  
8
−4
​,
u2=
  5  
−2
1
​,
and
u3=
  0  
1
0
.
Note that
u1
and
u2
are orthogonal. It can be shown that
u3
is not in the subspace W spanned by
u1
and
u2.
Use this to construct a nonzero vector
v
in
ℝ3
that is orthogonal to
u1
and
u2.
 
 
 

Question content area bottom

Part 1
The nonzero vector
v=enter your response here
is orthogonal to
u1
and
u2.
5 -2 1 R³ that is orthogonal to u₁ and ₂. Let u₁ = 4 8 4 42 and u3 0 Note that u₁ and u₂ are orthogonal. It can be shown that u3 is not in the subspace W spanned by u₁ and u₂. Use this to construct a nonzero vector v in The nonzero vector v = is orthogonal to u₁ and u₂.
Transcribed Image Text:5 -2 1 R³ that is orthogonal to u₁ and ₂. Let u₁ = 4 8 4 42 and u3 0 Note that u₁ and u₂ are orthogonal. It can be shown that u3 is not in the subspace W spanned by u₁ and u₂. Use this to construct a nonzero vector v in The nonzero vector v = is orthogonal to u₁ and u₂.
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