MATH 1B Final: math1B-fa2002-final-Wu-exam

Find a formula for the nth term of the sequence. 1, -1/16, 1/81, -1/256, 1/625,... Choose the correct answer below. an = (-1)n + 1/n4, n 1 an = (-1)n + 1/n4, n 1 an = (-1)n + 1/n5, n 1 an = (-1)n + 1/(n+1)4, n 1 an = 1/n5, n 1 an = 1/n4, n 1 an = 1/(n+1)5, n 1 an = (-1)n+1/n5, n 1

Let B = [-1 1 -1 1], [1 1 1 1], [1 1 -1 -1], [1 -1 -1 1] y = [-3 4 2 1] is B an orthogonal basis for R^4? How would we make on orthonormal basis from B?

Compute the determinant of the following matrices, use cofactor method. [A] = [1 1 1 1], [B] = [0 1 1 0], [C] = [1 -1 1 1] [0] = [1 1 1 1 1 0 1 0 0] [E] = [1 2 3 4 4 4 5 6 7] [F] = [1 2 3 4 5 6 7 0 0] [G] = [1 -1 0 0 -1 2 -1 0 0 -1 2 -1 0 0 -1 2] [H] = [2 1 0 0 1 2 1 0 1 1 2 1 1 1 1 2] Check the result using matlab!