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1. In each of the following settings, select the algorithm(s) that is(are) guaranteed to solve the stated problem. (a) Suppose A is any n X n nonsingular matrix and b E R\". Solve Ax : b. o Jacobi's algorithm on Ax : b GaussSeidel algorithm on Ax : b Gaussian elimination with partial pivoting on [A, b] and back substitution Gradient descent on the normal equations for A7 b Gradient descent on the normal equations for [:2] , [12] QR factorization of [A, b] and back substitution DDDDDDD None of the above (b) Suppose A E Rmxn, m > n, with linearly independent columns and b E Rm. Solve for the leastsquares solution of Ax : b. DDDEDDD Jacobi's algorithm on AX : b GaussSeidel algorithm on Ax : b Gaussian elimination with partial pivoting on [A, b] and back substitution Gradient descent on the normal equations for A, b Gradient descent on the normal equations for [i] , [g] QR factorization of [A, b] and back substitution None of the above (c) Suppose 4 l 0 0 1 4 1 0 A _ 0 1 4 1 0 0 1 4 and b is any vector in R4. Solve for the solution of Ax : b. DDDDDDD Jacobi's algorithm on Ax : b GaussSeidel algorithm on Ax = b Gaussian elimination with partial pivoting on [A, b] and back substitution Gradient descent on the normal equations for A, b Gradient descent 0n the normal equations for [i] , [g] QR factorization of [A, b] and back substitution None of the above (d) Suppose A is m x n, m