Question

show that the vectors(3,0,-3),(-1,1,2),(4,2,-2)and(2,1,1) are linearly dependent over R.

Answer 1

I don't know whether I understood your question right, but to show that the vectors are dependent you can:

1. Say that 4 vectors in R^3 are always dependent (because to have a basis for R^3 you only need 3 vectors)

2. Put the vectors in a matrix and try to invert it. You will see that the matrix is not square so that you can't invert it, thus it has dependent vectors.