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hwk2 - 2 Consider the following two matrices E = 8 2-1-4 0...

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CS 525 - Fall 2011 - Homework 2 * assigned 9/14/11 - due 9/21/11 Hand in an annotated diary file, constructed as outlined in the MATLAB Setup handout and in Homework 1. Your diary should contain a record of your session and should look something like the following: diary hwk2.lastname.firstname G=[1 2 -1 3; 2 1 3 5; 0 -3 4 -2]; . . . who . . . . . . diary off Be sure to write out the solution explicitly. For example, if you are asked for B - 1 , extract this matrix from the tableau, perform any necessary row and column permutations, and annotate your file clearly to indicate this matrix. 1. Let G = 3 - 1 2 - 3 - 2 - 5 3 - 1 - 3 0 2 0 - 2 2 - 3 . By using the Jordan exchange code ljx.m , find out how many linearly independent rows G has. Find out how many linearly independent columns G has. (You can do the latter by working with G 0 .) In both cases, if there are linear dependencies, write them out explicitly. * Hard copy to be submitted in class on the due date. No late homework accepted.

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Unformatted text preview: 2. Consider the following two matrices: E = 8 2-1-4 0 9 2 4 , F = 3 1 1 1 3 3-1 1 1 1 1 3-2 2-2 2 . Use ljx.m to ﬁnd the inverse of each matrix, if it exists. If the matrix is singular, show the linear dependence between the rows. 3. Do Exercise 2-4-6. (The data for this problem can be loaded using load ex2-4-6 .) 4. Do Exercise 2-3-5 by hand. 5. Do Exercise 2-4-8. (Make up a small matrix A with the required prop-erties in each case, and explain why it has those properties, and also give examples of b where necessary.) 6. Prove that the product AB of two square matrices is nonsingular if and only if both A and B are non-singular. Remember, that if and only if means you have to prove this both ways: if AB is invertible then show A and B must both be invertible. If A and B are invertible, how AB is invertible. 2...
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