Let B={b,,..., b,} be a basis for a vector space V. You will be proving the following by filling in the blanks: If the set of coordinate vectors u,la: u, a is linearly dependent in R", then the subset u,} is linearly dependent in V. You need only write the word for each blank on our quiz, but be organized so I can grade your work. (a) If the set of vectors {u,a: [u,]a} is linearly dependent in (b) then there exist scalars c,- (where at least one c; is non-zero), (c) such that = 0 the zero vector in R" (d) By the of the coordinate mapping: „[u,] =[c«]la+ +[c,u,]a=[qu, + +c, +c, ...+ pp (e) (Note: c,u, is a vector in (f) Because 0, R" = [0, ]a' we can see that from above and part (c) that we have [gu, + ..+c,u,] =[0, ]g• Initial if you agree
Let B={b,,..., b,} be a basis for a vector space V. You will be proving the following by filling in the blanks: If the set of coordinate vectors u,la: u, a is linearly dependent in R", then the subset u,} is linearly dependent in V. You need only write the word for each blank on our quiz, but be organized so I can grade your work. (a) If the set of vectors {u,a: [u,]a} is linearly dependent in (b) then there exist scalars c,- (where at least one c; is non-zero), (c) such that = 0 the zero vector in R" (d) By the of the coordinate mapping: „[u,] =[c«]la+ +[c,u,]a=[qu, + +c, +c, ...+ pp (e) (Note: c,u, is a vector in (f) Because 0, R" = [0, ]a' we can see that from above and part (c) that we have [gu, + ..+c,u,] =[0, ]g• Initial if you agree
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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