Question

Sabendo que 3u -4v=2w. Determinar a, b, c sendo u=(2,-1,c) v=(a,b-2,3) e w=(4,-1,0).?

Answer 1

3u - 4v = 2w 
3 . (2, -1, c) - 4 . (a, b - 2, 3) = 2 . (4, -1, 0) 
(6, -3, 3c) - (4a, 4b - 8, 12) = (8, -2, 0) 
(6 - 4a, -3 - 4b + 8, 3c - 12) = (8, -2, 0) 
(6 - 4a, 5 - 4b, 3c - 12) = (8, -2, 0) 

6 - 4a = 8 
-4a = 2 *(-1) 
4a = -2 
a = -2 / 4 
a = -1 / 2 

5 - 4b = -2 
-4b = -7 *(-1) 
4b = 7 
b = 7 / 4 

3c - 12 = 0 
3c = 12 
c = 12 / 3 
c = 4