Numerical analysis

1. a (15 pts) Determine the single-precision represeutation in IEEE b. (10 pts) Determine the decimal mumber that has the hesadecimal 2. a. (10 pts) Show that the function f()-19 has a zero in the b. (15 pts) Use the bisection method to find an approximation to format of the decimal number 27.875. IEEE format representation 4SED8000 interval (4,5) V19 to within 10-2 3. Consider the fanction rz)-4 -1-4z + 11. a. (10 pts) Show that f(x) has exactly one zero in the isterval 12.4, b. (15 pts) Use Newton's method to find the zero of f(x) in the interval 12.4). Perform only three iterations 4. Cossider 7 3 -1 -114 a. (15 pts) Find the matrix fnctorization A - LU,where L is lower b. (10 pts) Use this decomposition of A to solve Az - b, where triangular and U is upper triangular b 3,-4. 5. Consider the system of linear equations Tri +312-13 + 274 = -1 a. (13 pts) Using the Jacobi iterative method, solve the given system b. (12 pts) Using the Gauss-Seidel iterative method, solve the given 6. (25 pts) Use Gaussian elimination with backward substitution to solve of linear equations. Perform only three iterations. system of linear equations. Perform only three iterations. b, where the following system Ar A -1 3-1 and b 0 -1 2