I need help solving the following questions.

1. (10 points) For the given vectors a and b (see the figure below), construct the following vectors: a-1b, b+la, b-2a. (Draw neat diagrams; label vectors appropriately). a b Figure 1The diagram below shows a few vectors lying in some plane P. Answer the following questions concerning these vectors (do not forget to substantiate your answers). a) Which of the following vectors is a basis in the line spanned by j: i, b, e,, v=(e22e.) ? For every one of these vectors that is a basis in that line, nd the coordinate of j in this basis. b) Which of the following sets form a basis in the plane P: {121'}, {111'}. {DJ}. {em}, {Gulf} '-' c) For every set from the section (b) that is a basis in P, nd the coordinates of a in this basis. (1) Which of the sets listed in section (b) are linearly independent? e) Which of the sets listed in section (b) span P? 3. ( 10+15 points) For each of the fol10wing sets of vectors determine whether it is a basis in R3. If a set is a basis, find the coordinates of a = (0, l, 3) in this basis. 2 0 l 01 1 0] "a) -3,5; b) 0,1,l;c) 0,1,0 4 6 1 21 l 21