5. (10 pt) Consider the basis B of R2 consisting of vectors -4 -1 -6 and...
Both Problems (1 pt) Consider the basis B of Ra consisting of vectors and Find x in R- whose coordinate vector relative to the basis B is [x]] = X = [-121 (1 pt) The set B = 3 | } is a basis for R2. 12 Find the coordinates of the vector x = relative to the basis B: [x]B =
(1 point) Consider the basis B of R consisting of the vectors and Note: These vectors are written in terms of the standard basis, E. You know the following about e R2: - [ 6 B Find [피e. TE (1 point) Consider the basis B of R consisting of the vectors and Note: These vectors are written in terms of the standard basis, E. You know the following about e R2: - [ 6 B Find [피e. TE
Previous Problem List Next (1 point) Consider the ordered basis B of R consisting of the vectors that order). Find the vector x in R2 whose 4 and (in coordinates with respect to the basis B are
set2: Problem 2 Previous Problem Problem List Next Proble (1 point) Consider the basis B of R2 consisting of vectors and -2 Find 료 in R2 whose coordinate vector relative to the basis B is B--s Preview My Answers Submit Answers You have attempted this problem 0 times. You have unlimited attempts remaining. Project
(1 point) Let B be the basis of R2 consisting of the vectors and let C be the basis consisting of Find a matrix P such that c = P8 for all in R? 4/29 -19/29 P- -1/29 12/29
2 Problem 6: (12.5 points) Consider the basis B-( | , I) of R2. a) Find the B-coordinate vector [vB of v - (4,5) b) Find the change of coordinates matrix from the standard basis coordinates to the coordinates relative to the basis B
5. For parts (a)-(d) below, consider the set of vectors B = {(1,2), (2, -1)}. (a) (2 points) Demonstrate that B is an orthogonal set in the Euclidean inner product space R2. (b) (3 points) Use the set B to create an orthonormal basis in the Euclidean inner product space R2 (e) (7 points) Find the transition matrix from the standard basis S = {(1,0),(0,1)} for R2 to the basis B. Show all steps in your calculation. (d) (7 points)...
ぱ] in R2 relative to the basis B = { 17 } 6. Find the coordinate vector of x =
1) for R2 Given the vectors b1,b2, C1, and cz. B = {b1,b2} is a basis for R2C = {C1,C2} is a basis b = [i.bz = [33],4 = (-2) c2 = [4] (a) Find the change of coordinates matrix to convert from B to C. (b) Find the coordinate vectors [x]B, [x]c, lyle and [ylc given x = [11] y = [12]
Problem 6 A bilinear pairing on R2 is given on basis vectors by <ei, ei >= 13; <ei, e2 >=< e2, ej >= 7; <e2,e2 >= 26 a) [3 pts) Find the matrix representation of the pairing. b) (4 pts) Explain why the bilinear pairing defines an inner product. c) [3 pts) If v = [5 – 3]T, find a non-zero vector w with < v, w >= 0