-1 16. A = -1 2 -2 -2 Use EROs to reduce A to an upper triangular matrix, and NOW O then use this to find the determinant of A. 0 -1 17. A is a 3 x 4 matrix and the RREF of A is 0 1 1 0 Write the general solution to 0 0 the system Ax = 0 in parametric form. 18. A polynomial p(x) in P; has the form p(x) = a + bx + cx? + dx3, where a, b, c, de R. Write a system of equations associated with the equations p(1) = 0 and p(-1) = 0, and use this system to find basis for the subspace of P3 consisting of all polynomials p(x) for which p(1) = 0 and p(-1) = 0. 19. H = span(x2 - x, x2 + 1}. a. Show that B = (x2 - x, x2 + 1) is a basis for H. b. p(x) E H and [p(x)Is = (3 )- p(x) = 2x + 3y + z = 2 20. Find the general solution to the system -x - 2y-2=-1 2x - y - 32 = 2 2 21. A = 4 0 2 a. Determine the value(s) of x for which A is invertible. b. Substitute the smallest value of x for which A is not invertible, and give a basis for Col A. 1 2 11 22. Suppose A is an invertible 3 x 3 matrix and A-1 = 13 -1 2 Solve the system 12 Ax = (-1) 23. A = ( ). Use elementary row operations to find the inverse of A