Problem 5: Let V and W be vector spaces and let B = {V1, V2, ..., Un} CV be a basis for V. Let L :V + W be a linear transformation, and let Ker L = {2 € V: L(x)=0}. (a) If Ker L = {0}, show that C = {L(v1), L(02), ..., L(vn) } CW is a linearly independent set in W. (b) If C = {L(01), L(V2),..., L(Un)} C W is a linearly independent set in W,...
Are the functions fi (x) = ex+4 and fz(x-er-5 linearly dependent or independent? A. Linearty dependent OB. Linearly independent Which of the following best describes the correct choice for part (a)? (Carefull) 0 A. Since the only solution to cfı + c/2 = 0 is ci = c2-0. B. Since the Wronskian equals zero for at least one x on (-o, o). C. Since the Wronskian never equals zero on (-oo, oo). D. Since the functions are scalar multiples of...
(1) Let u = (-1,2) and v = (3, 1). (a) (5] Find graphically the vector w = (2u - v). (b) (5] Find algebraically the vector z=3u - 2 (2) (a) [5] Write u ='(1, -5, -1) as a linear combination of v1 = (1,2,0), v2 = (0,1,-1), V3 = (2,1,1). (b) (5] Are the 4 vectors u, V1, V2, V3 linearly independent? Explain your answer. (C) (5) Are the 2 vectors V, V3 linearly independent? Explain your answer....
my solutions say linearly independent but i dont understand why 4. (5 pts) Let zu(e) = (2-1), sz(t) = [et] Determine whether the vector functions are linearly dependent or linearly independent on (-0,00). ww/xix.7(4) = fet to +-+-0 W[X, Xz] (t) = 0
1. Suppose Z N(0, 1) ει ~ N(0, ơÐ €2 ~ N(0,03) independent and let (a) 12 pts] Under what conditions (if an (b) [2 pts] Determine the covariance of Yi and Y2. Under what conditions (if any) are they y) are Yǐ and Y2 exchangeable? Justify your answer. (marginally) independent? 1. Suppose Z N(0, 1) ει ~ N(0, ơÐ €2 ~ N(0,03) independent and let (a) 12 pts] Under what conditions (if an (b) [2 pts] Determine the covariance...
Problem 1 1. Let xi ( t): qekit be K₂ t and 22 (+) Cekit de Kzt q. Compute w [X, X ] (t) a, b, c, d make b. What conditions on linearly dependent x, and 2 c. What conditions on t make my and to linearly dependent?
Problem 4 (1 point) Let 9 -9 3 Are the vectors vi, v2. and vs linearly independent or linearly dependent? linearly dependent If the vectors are linearly independent, enter 0 in every answer blank since those are only the values that make the equation below true. If the vectors are linearly dependent, find scalars, not all 0, which make the equation below true -167 -15 12+ Problem 5
Please show work thank you! Taekıt Let ci(t) = and 22(t) = [cekit (dekat I bekat (a) (6 points) Compute W[71,22](t) (b) (2 points) What conditions on a, b, c, d make ci and 22 linearly dependent? (c) (2 points) What conditions on t make wi and linearly dependent?
8. (15 points) Let A be a 4 x 5 matrix. If a, a, and 4 are linearly independent and a3 = a1 + 2a2, a5 = 2a - a2 +3a4 determine the reduced echelon form of A.
Exercise 5 Let z and y be linearly independent vectors in R" and let S- span(,y). We can use r and y to define a matrix A by setting (a) Show that A is symmetric (b) Show that N(A) S (c) Show that the rank of A must be 2. Exercise 5 Let z and y be linearly independent vectors in R" and let S- span(,y). We can use r and y to define a matrix A by setting (a)...