Let v = [1 3 -3] and consider the subspace of R³ spanned by the first two columns of 18 B 4 17 -3 = 1 -4 -1 1 Express these first two columns as vectors, call them u₁ and u2 by determining their transposes then normalize each of them ||u₁|| and ||u2||. find the inner products Write the projection of v onto the subspace: U1 + |||u₁|| U1 + ||u₂|| ՂԱԶ ՂԱԶ

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let v =
B
=
1 3 -3] and consider the subspace of R³ spanned by the first two columns of
4
17 3
1
- 1
0
1
Express these first two columns as vectors, call them u₁ and u₂ by determining their transposes
then normalize each of them ||u1|| and ||u2||.
- 4
0
find the inner products
<v, u1>
<V, U2
Write the projection of v onto the subspace:
U₁ +
< V, U1
||u₁||
U1
+
<V, U2
||u₂||
ՂԱԶ
ՂԱշ
Transcribed Image Text:Let v = B = 1 3 -3] and consider the subspace of R³ spanned by the first two columns of 4 17 3 1 - 1 0 1 Express these first two columns as vectors, call them u₁ and u₂ by determining their transposes then normalize each of them ||u1|| and ||u2||. - 4 0 find the inner products <v, u1> <V, U2 Write the projection of v onto the subspace: U₁ + < V, U1 ||u₁|| U1 + <V, U2 ||u₂|| ՂԱԶ ՂԱշ
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