2. For this problem, you should only use the definition of a basis, no tricks involving the dimension of a vector space. Consider the following set of vectors S = 1 1 2 3 -{E)-(e)} (a) Show that S is not a basis for R³ by showing that it fails one of the defining properties of bases. (b) Construct a basis for R³ using S and the methods covered in class. You must also show that your supposed basis satisfies the defining properties of bases.
2. For this problem, you should only use the definition of a basis, no tricks involving the dimension of a vector space. Consider the following set of vectors S = 1 1 2 3 -{E)-(e)} (a) Show that S is not a basis for R³ by showing that it fails one of the defining properties of bases. (b) Construct a basis for R³ using S and the methods covered in class. You must also show that your supposed basis satisfies the defining properties of bases.
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:2.
For this problem, you should only use the definition of a basis, no tricks involving the dimension of a
vector space.
Consider the following set of vectors
S =
1
1
2
3
-{E)-(e)}
(a) Show that S is not a basis for R³ by showing that it fails one of the defining properties of bases.
(b) Construct a basis for R³ using S and the methods covered in class. You must also show that your
supposed basis satisfies the defining properties of bases.
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