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planation. 20. If V is a vector space of dimension three and W is a subspace of V then the dimension of W is two.

planation. 20. If V is a vector space of dimension three and W is a subspace of V then the dimension of W is two.

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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1 -1)’(0 0 | In exercises 20 - 24 answer true or false and give an explanation. 20. If V is a vector space of dimension three and W is a subspace of V then the dimension of W is two. 21. If W is a subspace of a vector space V, the dimension of W is three, and (w1, w2, w3) is linearly independent from V then (wi, w2, W3) is a basis of W. 22. A basis for R³ can be contracted to a basis of R“. 23. A basis of M2x2(R) can be extended to a basis of M2x3(R). 24. A basis of R2[x] can be extended to a basis of R3[r].
Transcribed Image Text:1 -1)’(0 0 | In exercises 20 - 24 answer true or false and give an explanation. 20. If V is a vector space of dimension three and W is a subspace of V then the dimension of W is two. 21. If W is a subspace of a vector space V, the dimension of W is three, and (w1, w2, w3) is linearly independent from V then (wi, w2, W3) is a basis of W. 22. A basis for R³ can be contracted to a basis of R“. 23. A basis of M2x2(R) can be extended to a basis of M2x3(R). 24. A basis of R2[x] can be extended to a basis of R3[r].
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