Question 2 Let B {V1, V2, ... , vn} be a basis for a vector space V and define vn+1 € V by Vn+1 = a1V1 + a2V2 + . .. + a„Vn, where a; E R and a¡ # 0 for i = 1, 2, . . . , n. i. Prove: C = {v2, V3, ... , Vn, vn+1} is a basis for V. Fix the given order of vectors, that is, B = (V1, V2, ... , Vn) and C = (v2, V3, . , Vn, Vn+1) so that henceforth these are ordered bases of V. ii. Find [I]. iii. Find det [7]g.
Question 2 Let B {V1, V2, ... , vn} be a basis for a vector space V and define vn+1 € V by Vn+1 = a1V1 + a2V2 + . .. + a„Vn, where a; E R and a¡ # 0 for i = 1, 2, . . . , n. i. Prove: C = {v2, V3, ... , Vn, vn+1} is a basis for V. Fix the given order of vectors, that is, B = (V1, V2, ... , Vn) and C = (v2, V3, . , Vn, Vn+1) so that henceforth these are ordered bases of V. ii. Find [I]. iii. Find det [7]g.
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 2
Let B
{V1, V2, ..., Vn} be a basis for a vector space V and define vn+1 € V by
Vn+1 = A1V1 + a2V2 + . . . + a„Vn, where a; € R and a; # 0 for i = 1, 2, . , n.
i. Prove: C =
{V2, V3, ... , Vn, Vn+1} is a basis for V.
Fix the given order of vectors, that is, B =
so that henceforth these are ordered bases of V.
(V1, V2, ..., Vn) and C = (v2, V3, .. . , Vn, Vn+1)
ii. Find [I].
iii. Find det [I.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F947394f8-c939-4c1f-b403-7ecbbe117a89%2F77b7bc54-0c4d-4326-bddc-467e9b7862da%2Fpf0ns9y_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 2
Let B
{V1, V2, ..., Vn} be a basis for a vector space V and define vn+1 € V by
Vn+1 = A1V1 + a2V2 + . . . + a„Vn, where a; € R and a; # 0 for i = 1, 2, . , n.
i. Prove: C =
{V2, V3, ... , Vn, Vn+1} is a basis for V.
Fix the given order of vectors, that is, B =
so that henceforth these are ordered bases of V.
(V1, V2, ..., Vn) and C = (v2, V3, .. . , Vn, Vn+1)
ii. Find [I].
iii. Find det [I.
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