exercises 1 and 2, all parts

and L2. 1. a. Compute (by hand) the products LiL2 and L2L1 of L1 = [1 0 0; -1/2 1 0; 1/2 0 1] and L2 = [1 0 0;0 1 0;0 1/4 1]. b. If A is a 3 x 3 matrix, describe the row operations that would be performed on A if it were premulti- plied by Li; if it were premultiplied by L2; and if it were premultiplied by L2L1. c. Find the inverses of L1 d. Let A=[1 1 1;1/2 3/2 3/2; -1/2 - 3/4 1/4]. Compute L2L1A. e. What is the LU decomposition of A? Explain how you are using your answers from the previous parts of this problem to answer this question. 2. a. Find the LU decomposition of the matrix A= [1 2 3;4 5 6;7 8 8] (by hand; follow Example 2.3.2). b. Use the LU decomposition of A to solve the linear system Ax = b, where b = (1,2,3)