B 4. Consider two vectors 71 = 2 and 2 = (a) Find a vector which is orthogonal to both of these vectors.Call it w (b) Verify that this vector is linearly independent with 71 and 72. (c) Now remaining within the subspace spanned by 71 and 72, replace 71 with a vector that is orthogonal to 72. Call it 7. Show that 7 is still orthogonal to w. [1]

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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4. Consider two vectors v1=
2 and 72 = |1
(a) Find a vector which is orthogonal to both of these vectors.Call it w
(b) Verify that this vector is linearly independent with 71 and 2.
(c) Now remaining within the subspace spanned by 71 and V 2, replace 71 with a vector
that is orthogonal to 72. Call it . Show that d is still orthogonal to w.
(d) 72, w and d form an orthogonal basis. Express the vector
as a linear combination
of this basis
Transcribed Image Text:1 1 4. Consider two vectors v1= 2 and 72 = |1 (a) Find a vector which is orthogonal to both of these vectors.Call it w (b) Verify that this vector is linearly independent with 71 and 2. (c) Now remaining within the subspace spanned by 71 and V 2, replace 71 with a vector that is orthogonal to 72. Call it . Show that d is still orthogonal to w. (d) 72, w and d form an orthogonal basis. Express the vector as a linear combination of this basis
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