My task is to show that the set of vectors: $\bf x_1, x_2, x_3, x_4$ where
$\bf x_3=[1,t,t^2]$ and
$\bf x_4=[t+2,t+1,t^2+1]$ are linearly dependent. (Note: $x_i$ can also be written in matrix format.)
To show that they are linearly dependent I form the equation:
$\bf c_1x_1+c_2x_2+c_3x_3+c_4x_4=0$ and will show that there is a nonzero solution to it. That is I will show that aside from $\bf c_1,c_2,c_3,c_4=0$ there is some other solution to it.
However solving puts me in a system of 3 equations in 4 unknowns which seems new to me. They are:
Can someone help me to find a non trivial solution to the given system of equation? or Will you help me showing that the 4 vectors above are linearly dependent?
Thank you so much for your help.