For the subspace below, (a) find a basis, and (b) state the dimension 9a + 18b-3c 12a-4b-4c - 3a + 5b + c - - 3a+b+c a, b, c in R a. Find a basis for the subspace. A basis for the subspace is . (Use a comma to separate vectors as needed.) e vettaikainggo zenbait mangfo

The coordinate vector of the vector (-4,3,1) in the basis B = {u= (1,1,1); v = (1,0,1); w= (0,0,1) } is: O A. (1,-4,3) OB. (-4,3,1) OC. (3,- 7,5) O D. (2,-1,1)

Either find the coordinates of the vector relative to basis B, or find the original vector from the coordinates relative to basis B. (a) v = (3,5,10); B = {(1,0,−1), (2, 1, −1), (-2, 1,4)} for R³. (b) v = (13,54); B = {(1,0), (0, 1)} for R². (c) [v]B = (10,-1, 4); B = {(1,0,−1), (2, 1, −1), (−2, 1,4)} for R³.

Let the basis B = {b1, b2} and basis C = {c1, c2} where vectors b1 = (7 -2). b2 = 2 -1 , c1 = 4 1  c2= 5 2 Find the change of coordinates matrix from B to C. (b) Find the change of coordinates matrix from C to B.

Find the vectorx determined by the given coordinate vector [x]g and the given basis B. 4 -2 - 1 B = .[X]B= 0. -1 0. -2 X = (Simplify your answers.) Enter your answer in the edit fields and then click Check Answer. Clear

Calculate the cross product. (5i - 9j+7k) x (i+j-7k) = ai + bj + ck (Give your answer using component form or standard basis vectors. Express numbers in exact form. Use symbolic notation and fractions where needed.) (a, b, c) =