3. Consider v₁ = 1 2 1 0 7 V2: 1 and v3 = (a) Find the angle between ₁ and v₂. (b) Find all vectors in R4 that are orthogonal to v₁, v2 and v3. 1 in R4. (c) Use Gram-Schmidt process to transform {v1, V2, V3} into a set of orthonormal 1 2 3 a vectors {w₁, w2, w3). Given that u = E span {w₁, W2, W3}, find the value of a and write u as a linear combination of w₁,w2 and w3.
3. Consider v₁ = 1 2 1 0 7 V2: 1 and v3 = (a) Find the angle between ₁ and v₂. (b) Find all vectors in R4 that are orthogonal to v₁, v2 and v3. 1 in R4. (c) Use Gram-Schmidt process to transform {v1, V2, V3} into a set of orthonormal 1 2 3 a vectors {w₁, w2, w3). Given that u = E span {w₁, W2, W3}, find the value of a and write u as a linear combination of w₁,w2 and w3.
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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Transcribed Image Text:3. Consider v₁ =
1
2
1
7
V2:
1
and v3 =
in R₁.
(a) Find the angle between ₁ and v₂.
(b) Find all vectors in R4 that are orthogonal to v₁, v2 and v3.
1
(c) Use Gram-Schmidt process to transform {v1, V2, V3} into a set of orthonormal
1
2
vectors {w₁, w2, w3). Given that u =
3
a
E span {w₁, W2, W3}, find the
value of a and write u as a linear combination of w₁,w2 and w3.
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