Question

show that there not exist scalars C1,C2,C3 such that C1(-2,9,6) +C2(-3,2,1)+C3(1,7,8) =(0,5,4)
by using Cramer's rule I get C1 = 11/21; C2 = 62/63; C3= 4/21. It is contradict with the requirement. I don't know why. anybody help me, please

Answer 1

try showing that the matrix on the left is not invertible

Answer 2

wolfram says no solution exist .. possibly you made some error
http://www.wolframalpha.com/input/?i=solve+x%28-2%2C9%2C6%29+%2B+y%28-3%2C2%2C1%29%2B+z%281%2C7%2C8%29+%3D%280%2C5%2C4%29
or show that these rows are linearly dependent

Answer 3

det A = 69, how can it be not invertible?

Answer 4

it is invertible with A^-1 =[0]

Answer 5

seems that the matrix is really invertible and the solutions really exist.
http://www.wolframalpha.com/input/?i=solve+%7B%7B-2%2C-3%2C1%7D%2C%7B9%2C2%2C7%7D%2C%7B6%2C1%2C8%7D%7D.%7B%7Bx%7D%2C%7By%7D%2C%7Bz%7D%7D+%3D+%7B%7B0%7D%2C%7B5%7D%2C%7B4%7D%7D