.. ' . . l: \\ . r ,y _ Problem 3. A matrix A = (v1, ..., v5) with column vectors v1, ..., v6 6 R4 has row reduced form (a) Do the vectors v1, ..., v6 span R4? (b) Are the vectors v1, ..., v6 linearly independent? (0) What is the row reduced form of the matrix C = (v3, v4, v5, v5)? (d) Write v5 as a linear combination of v1, v2 and v4. (e) Show that the sequence v1, v3, v4, vs is a basis of R4. (f) What are the coordinates of v5 in the basis v1, v3, v4, v6? (g) If a vector v has coordinates (1, 2, 3, 4) in the basis v1, v3, v5, v6, what are the coordinates of v in the basis v1, v3, v4, v5? 1