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Quiz Solutions for ECE S-510, Winter 2006, Quiz #1, Exercises of Analytical Techniques

The solutions to quiz #1 for the ece s-512 vector calculus course held in winter 2006. The quiz covers topics such as spanning a space, finding vector norms, orthogonality, and expressing a vector as a linear combination of two given vectors. Students are encouraged to use this document as a study aid for reviewing the concepts covered in the quiz.

Typology: Exercises

2012/2013

Uploaded on 05/18/2013

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Winter 2006 Quiz # 1 ECE S-510
You are given the following two vectors r1 = [1 2]t and r2 = [2 1]t.
(a) Can you span the R2 space using r1 and r2? Why?
(b) Find ||r1|| and ||r2||. Are r1 and r2 orthogonal? Why?
(c) If you are given the vector r = [3 1]t , can you express r as a linear combination
of r1 and r2, i.e., r = C1 r1 + C2 r2? Why? Find C1 and C2. Why aren’t C1 and C2
just the respective projections of r onto r1 and r2?
(d) If we want to span the R2 space using two orthonormal vectors
φ
1 and
φ
2 such
that r1 is in the direction of
φ
1. Find
φ
1 and
φ
2 in terms of r1 and r2.
(e) If we want to approximate r in part (c) by either r1 or r2, which one would you
use and why?
_______________________________
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Download Quiz Solutions for ECE S-510, Winter 2006, Quiz #1 and more Exercises Analytical Techniques in PDF only on Docsity!

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Winter 2006 Quiz # 1 ECE S-

You are given the following two vectors r 1 = [1 2]t^ and r 2 = [2 1]t. (a) Can you span the R^2 space using r 1 and r 2? Why? (b) Find || r 1 || and || r 2 ||. Are r 1 and r 2 orthogonal? Why? (c) If you are given the vector r = [3 1]t^ , can you express r as a linear combination of r 1 and r 2 , i.e., r = C 1 r 1 + C 2 r 2? Why? Find C 1 and C 2. Why aren’t C 1 and C 2 just the respective projections of r onto r 1 and r 2? (d) If we want to span the R^2 space using two orthonormal vectors φ 1 and φ 2 such that r 1 is in the direction of φ 1. Find φ 1 and φ 2 in terms of r 1 and r 2. (e) If we want to approximate r in part (c) by either r 1 or r 2 , which one would you use and why?


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