(g) Because the coordinate mapping is [qu, + ..+c,u, ] =[0,]a implies qu, + .+c,u, = 0, . ...+ C. v ]B (h) Therefore, the set of vectors is

Extracted text: (g) Because the coordinate mapping is [qu, + ..+c,u, ] =[0,]a implies qu, + .+c,u, = 0, . ...+ C. v ]B (h) Therefore, the set of vectors is


Extracted text: 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,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,] 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: G[u,]a+ +Cpup си. ...+C u + + + -.. (e) (Note: c,u, is a vector in (f) Весause 0. R" =|0, la, we can see that from above and part (c) that we have [qu, +.+c,u,]=[0, la: Initial if you agree +c̟u, pp ]B