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Let B = Select all correct options. dim(V) = m. IfC = (w²₁, There exists a coordinatisation map from V to Rm. None of the above. V₁, V₂,...,Um be a basis of V. wi, w,..., w is also a basis of V, then n = m.

Let B = Select all correct options. dim(V) = m. IfC = (w²₁, There exists a coordinatisation map from V to Rm. None of the above. V₁, V₂,...,Um be a basis of V. wi, w,..., w is also a basis of V, then n = m.

Advanced Engineering Mathematics
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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Let B = (v₁, v₂,..., Um Select all correct options. dim(V) = m. If C = wi, w, be a basis of V. None of the above. w is also a basis of V, then n = m. There exists a coordinatisation map from V to Rm.
Transcribed Image Text:Let B = (v₁, v₂,..., Um Select all correct options. dim(V) = m. If C = wi, w, be a basis of V. None of the above. w is also a basis of V, then n = m. There exists a coordinatisation map from V to Rm.
Expert Solution
Step 1

from the given data 

the basis B has dimension m

so the dimension of V is also m 

dim(V) = m

option 1 is correct

we know that if there are two basis for a vector with different dimensions

then the dimensions of both basis are equal

so, if C is also a basis of V then n=m

option 2 is correct

from the above data we can say that 

there exists a coordination map from V to R^m

option 3 is correct

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