24. Let S be a basis for an n-dimensional vector space V. Show that if v, v2. ...,v, form a linearly independent set of vectors in v, then the coordinate vectors (v)s. (V2)s. .... (v,)s form a linearly independent set in R", and conversely.
24. Let S be a basis for an n-dimensional vector space V. Show that if v, v2. ...,v, form a linearly independent set of vectors in v, then the coordinate vectors (v)s. (V2)s. .... (v,)s form a linearly independent set in R", and conversely.
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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![24. Let S be a basis for an n-dimensional vector space V. Show that if V1, V2, ..., v, form a
linearly independent set of vectors in V, then the coordinate vectors (v)s. (V2)s..... (v,)s
form a linearly independent set in R", and conversely.
25. Using the notation from Exercise 24, show that if v, v2, ... v, span V. then the coordinate
vectors (v,)s. (v2)s.. (v,)s span R", and conversely.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8aac5adb-6dab-4fd2-b24a-f65c2c7bd6c3%2F0bb3bf2b-2415-4182-91f2-dc9130bcf8ae%2Fp3bd8n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:24. Let S be a basis for an n-dimensional vector space V. Show that if V1, V2, ..., v, form a
linearly independent set of vectors in V, then the coordinate vectors (v)s. (V2)s..... (v,)s
form a linearly independent set in R", and conversely.
25. Using the notation from Exercise 24, show that if v, v2, ... v, span V. then the coordinate
vectors (v,)s. (v2)s.. (v,)s span R", and conversely.
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