# Thread: vectors help...

1. ## vectors help...

Let A = [6 2 11] B = [0 -4 6] and C = [-3 -2 -4]

Determine whether the three vectors listed above are linearly independent or linearly dependent.

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.

Ok so i have figured out that these vetors are linearly dependent...but i cant figure out the linear relation...can smn help me solve that part..thanks

2. Originally Posted by omibayne
Let A = [6 2 11] B = [0 -4 6] and C = [-3 -2 -4]
Determine whether the three vectors listed above are linearly independent or linearly dependent.
Is the matrix $\displaystyle \left( {\begin{array}{rrr} 6 & 2 & {11} \\ 0 & { - 4} & 6 \\ { - 3} & { - 2} & { - 4} \\ \end{array} } \right)$ singular?

3. Originally Posted by Plato
Is the matrix $\displaystyle \left( {\begin{array}{rrr} 6 & 2 & {11} \\ 0 & { - 4} & 6 \\ { - 3} & { - 2} & { - 4} \\ \end{array} } \right)$ singular?
yes, it is singular (determinant is zero)....but i need to know how to find the linear relation...

4. Originally Posted by omibayne
Let A = [6 2 11] B = [0 -4 6] and C = [-3 -2 -4]

Determine whether the three vectors listed above are linearly independent or linearly dependent.

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.

Ok so i have figured out that these vetors are linearly dependent...but i cant figure out the linear relation...can smn help me solve that part..thanks
If they are independent, then there exist numbers a, b, c, not all 0, such that aA+ bB+ cC= 0.
aA+ bB+ cC= [6a 2a 11a]+ [0 -4b 6b]+ [-3c -2c -4c]= [6a-3c 2a-4b-3c 11a+6b-4c]= [0 0 0]

You are really just being asked to solve the equations 6a- 3c= 0, 2a-4b-3c= 0, and 11a+6b-4x= 0.