Answer Happy

Problem 4. (6 points) Consider the matrix 1 0 0 -2 -3 0 1 4 C = 4 -6 4 -16 -16 16 16 -7 -4 -4 The MATLAB code to produce C is given by: C = [1,0,0,0,0,0; -2, -3,0,0,9,0; 1,4,4,0,-16,8; 4,-16,-16, -6,52,-20; -6,16,16,6, -52,20; -7,-4,-4,0,16,-8] Let S = {a, b, c, d, e, f} where a(x) = 1 - 2x + x² + 4x³ 6x4 7x5, b(x) =-3x + 4x² 16x³ + 16x4 4x5, c(x) = 4x² - - 16x³ + 16x¹ − 4x5, d(x) = −6x³ + 6x¹, e(x): = 9x - 16x² + 52x³ — 52x¹ + 16x5, f(x) = 8x². 20x³ + 20x¹ - 8x5. a. Find the reduced row echelon form of C: 0 0 0 0 9 0 0 -16 8 -6 52 -20 6 -52 20 0 16 -8
b. Write down a set of vectors from S that forms a basis for span (S): { Enter your answer as a list of vectors separated by commas, e.g. a,b,c. Write the polynomials just as a, b etc., not as a(x). c. What is the dimension of span (S)? d. Are the vectors {a, b, d} linearly dependent or independent? ? e. Are the vectors {b, c, d, e} linearly dependent or independent? ? f. For a linearly dependent set from question (d) or (e), write one of the vectors as a linear combination of the others. It there were no linearly dependent sets, leave it blank.