I am trying to solve these following problem i pick from a book i am confuse as to how to approach the question i will appreciate your help or solution
Which of the following sets of vectors in P2 are linearly dependent?
- 2-x+4x2, 3+6x +2x2, 2+10x - 4x2
- 3+x+x2, 2-x+5x2, 4-3x2
- 6-x2, 1+x+4x2
NB:X2 the 2 infront of the x's are superscripts
Since you are attempting to do a problem involving "dependent" and "independent" vectors you surely must have seen the definition of "dependent" so just check whether those are satisfied.
Do there exist three non-zero numbers a, b, and c, such that a(2-x+4x^2)+ b(3+6x +2x^2)+ c(2+10x - 4x^2)= 0. One way to do that to collect the coefficients of the same powers and set the coefficients equal to 0 to get three equations in a, b, and c. Another way would be to set x equal to any three numbers you like to get to get three equations.