SOLUTION: find the coordinate vector for w relative to the basis S={ u1, u2} for R^2. a) u1 = (1,0), u2 = (0,1); w = (-4,3) b) u1 = (1,-1), u2 =(2,5); w = (3,7)

Algebra ->  College  -> Linear Algebra -> SOLUTION: find the coordinate vector for w relative to the basis S={ u1, u2} for R^2. a) u1 = (1,0), u2 = (0,1); w = (-4,3) b) u1 = (1,-1), u2 =(2,5); w = (3,7)      Log On


   

Question 851477: find the coordinate vector for w relative to the basis S={ u1, u2} for R^2.
a) u1 = (1,0), u2 = (0,1); w = (-4,3)
b) u1 = (1,-1), u2 =(2,5); w = (3,7)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
a)w=-4%2Au1%2B3%2Au2
b)w=a%2Au1%2Bb%2Au2
x:3=1a%2B2b
y:7=-1a%2B5b
Adding,
10=7b
b=10%2F7
Then,
a%2B20%2F7=3
a=21%2F7-20%2F7
a=1%2F7
w=%281%2F7%29%2Au1%2B%2810%2F7%29%2Au2