Determine whether the following vectors are linearly independent in P3 "not sure what P3 stands for maybe polynomial of third degree?"
I then create a matrix using the above relation where I get
The matrix i'm thinking if solving looks like this [0 1 1;0 0 0; 1 0 -2] I know the zero must be at the bottom so I switch things up and get [1 0 -2; 0 1 1;0 0 0]
When I actually solve it I get c2=-c3
which is a nontrivial solution, so I state that it is linearly dependent.
Is my work correct, and or is there a faster way to come up with the conclusion that it is linearly dependent?