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
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.