• Nov 22nd 2008, 12:32 PM
eiktmywib
A=[-2
-7
-1]

B=[-2
4
-3]

C=[0
6
-4]

and i'm supposed to determine if they're linearly depedent or independent
The vectors were written horizontally this time, as they often are in books, but that is just to save space. The problem is the same as if the vectors were written vertically.
If they are linearly dependent, determine a non-trivial linear relation - (a non-trivial relation is three numbers which are not all three zero.) otherwise, if the vectors are linearly independent, enter 0's for the coefficients, since that relationship always holds.

____A + _____B + ______C = 0

I have determined that it is linearly dependent... but I don't know how to solve for A, B, and C.
• Nov 23rd 2008, 12:20 AM
mr fantastic
Quote:

Originally Posted by eiktmywib
A=[-2
-7
-1]

B=[-2
4
-3]

C=[0
6
-4]

and i'm supposed to determine if they're linearly depedent or independent
The vectors were written horizontally this time, as they often are in books, but that is just to save space. The problem is the same as if the vectors were written vertically.
If they are linearly dependent, determine a non-trivial linear relation - (a non-trivial relation is three numbers which are not all three zero.) otherwise, if the vectors are linearly independent, enter 0's for the coefficients, since that relationship always holds.

____A + _____B + ______C = 0

I have determined that it is linearly dependent... but I don't know how to solve for A, B, and C.

If the vectors were dependent then it'd be possible to find a value of $\displaystyle \alpha$ and $\displaystyle \beta$ such that

$\displaystyle <-2, -7, -1> = \alpha <-2, 4, -3> + \beta <0, 6, -4>$.

Obviously $\displaystyle \alpha = 1$ is necessary but it's not possible to get a value of $\displaystyle \beta$.

The obvious conclusion is that A, B and C are NOT dependent, that is, they are independent.