Show your work and reasoning so that all your solutions are justified. 1) Show that the following set either spans or does not span R S = 1 9.(- ;)-(8) New Page 2) Show that the following set is linearly independent or show that it is linearly dependent. S = { ...."..New Page... 3) Find a basis for the following space. Verify that it is a basis by explicitly showing that the sequence you propose is linearly independent and that it spans S. X s = { y _ x - y - = =0} Z4) Find a basis for each space. Verify that it is a basis by showing that it spans the subspace and is linearly independent. a) The subspace M: {n+ bx+ cxzul 7 25+ c : 0} of 702. New Page b) This subspace of M 2x 2. ab Cd)sc_0} W_{[ 5) Is the following sequence of vectors a basis for R: ? Verify that it is, or show and explain why it is not a basis. 12 8 s: 2 17 New Page 6) Represent the vector f} as a column vector with respect to each of the two bases. f;_[3 I} A 1 1 1 1 2 1 Hm:WHBfZ