Question

Problem 4 A set of vectors is given by S = {V1, V2, V3} in R3 where eV1 = 1 5 -4 7 eV2 = 3 . eV3 = 11 -6 10 a) [3 pts) Show that S is a basis for R3. b) (4 pts] Using the above coordinate vectors, find the base transition matrix eTs from the basis S to the standard basis e. Then compute the base transition matrix sTe from the standard basis e to the basis S. c) [3 pts) If ev = 2 12 , compute sv (the coordinate vector of v with respect to the basis S). Use this to express v as a linear combination of the vectors in S.

Answer 1

5 5 n o 14 14 23 17 161 0 0 in So there row are 3 nan zero rows echelon form of A. Thus rank of is 3. = 3 => = 0 = Now from Rank, meelity therem! - Rank of A+ Hallity of A But Rank of A = 3 Hercity of a Ax = 0 has only trivial Bolletion. VI, V2, V3 of A are finearly for dependent, Also rank of A=3 Jombly AX= Solution for any BEIR BEIR . This columns of span IR. Honce set S={ 12 Ug? form a Basi's Thus Cclumns =B. has A for R.

80 6 비 4 1 || ㅋ (7 se g 35 65 14. 35 21 85 14. PS -93 85 3 Answer (C) 9 v= 19 [v] C. -4- [ugs = ste [Je formula 4 녀 F 2. 국 2. RS 12 화 14 85 85 는 4 85. 14. 85 - g 85 uJs 뾿 v = 0Vit을 뾿 -39 85 60 V3 Answer