1. Let "W" be the set of vectors of the form below. Show that "W" is a subspace of R4. You must show all of the necessary math and cite any relevant theorems. - 2r+2s - 3t s-t r-3s-2t 2r-s+ 3t

Find a basis for R2 that includes the vector (2,2).

Take this test to review the material in Chapters 4and Chapters 5. After you are finished, check your work against the answers in the back of the book. Write w=(7,2,4) as a linear combination of the vectors v1, v2 and v3 if possible. v1=(2,1,0), v2=(1,1,0), v3=(0,0,6)

Let v1, v2, and v3 be three linearly independent vectors in a vector space V. Is the set {v12v2,2v23v3,3v3v1} linearly dependent or linearly independent? Explain.