Consider the set C² : Z1, 2 Define the vectors of ū, ū, w E C² 6- () -1+ i) -2+i) 2 2i -1+3i We can create different vector spaces on the same set by using a different choice of scalars. In particular, we can define: • V to be the vector space of C² over R, where the scalars are elements of R • W to be the vector space of C² over C, where the scalars are elements of C Show that ej = (1,0)" and e (0, 1)T forms a basis of W and hence determine the || dimension of W. Find a basis of V and hence determine the dimension of V.
Consider the set C² : Z1, 2 Define the vectors of ū, ū, w E C² 6- () -1+ i) -2+i) 2 2i -1+3i We can create different vector spaces on the same set by using a different choice of scalars. In particular, we can define: • V to be the vector space of C² over R, where the scalars are elements of R • W to be the vector space of C² over C, where the scalars are elements of C Show that ej = (1,0)" and e (0, 1)T forms a basis of W and hence determine the || dimension of W. Find a basis of V and hence determine the dimension of V.
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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Question
Find basis and determine the dimension.
Transcribed Image Text:Consider the set C2 :
21,
Define the vectors of ū, ū, w E C²
2
-(")
2i
-1+i
-1+3i
-2+ i
We can create different vector spaces on the same set by using a different choice of scalars.
In particular, we can define:
• V to be the vector space of C2 over R, where the scalars are elements of R
• W to be the vector space of C2 over C, where the scalars are elements of C
Show that ej = (1,0)" and e
(0, 1)T forms a basis of W and hence determine the
dimension of W. Find a basis of V and hence determine the dimension of V.
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