proves from linear algebra.?

Question

Determine if the vectors v = (2, -2, 1) , u = (1, 1, 1) , w = (1, 0 ,1) are linearly independent or linearly dependent.
(Also please tell me a good website to learn this stuff easily, cuz my book is complicated and professor too :(

Answer 1

what book do you use... the book by Bernard Kolman is a simple one... it might help you...


to show whether they are linearly independent or not...
make av + bu + cw = 0

a(2,-2,1) + b(1,1,1) + c(1,0,1) = (0,0,0)

you now have 3 linear equations in 3 unknowns...
2a + b + c = 0
-2a + b = 0
a + b + c = 0

from the first and third... subtracting...
a = 0
from the second...
b = 0
thus we can also have c = 0

the set is linearly independent because the only solution is a=b=c=0.


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Answer 2

if for some a, b, c multipliers (not all 0), au + bv + cw = (0,0,0), then they are not independent. so we try to solve the system:
1) 2a + b + c = 0
2) -2a + b = 0
3) a + b + c = 0

adding eq 1 & 2,
4) 2b + c = 0

adding 2(eq 3) & eq 2,
5) 3b + 2c = 0

subtracting eq 5 from 2(eq 4),
6) b = 0

using 4), c = 0, and then using 3), a = 0, so yes, u, v, w are independent.

Answer 3

Your smart. Can you go to my page and answer my calculus question? thanks?

Sorry. i cant help.