MAT 335-1

Homework Assignment #6

Hand in Wednesday, October 10, 2007

Let

In Problems #1-6, use A, B , , and to make the indicated calculations by hand and show your work. Checking with MATLAB is a good idea, though.

1.

2.

3. and

4.

5.

6.

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7. Let A and B be n´n matrices. Prove that . [Hint: Use Theorem 3, p. 113.]

8. Let A and B be n´n matrices. Use the definition of matrix addition to prove step-by-step, with reasons, that .

9. Suppose A is an n´n invertible matrix. Prove that . [Model your reasoning after the way we proved in class that .]

10. Suppose C is invertible and that . Solve for A in terms of B and C, showing each step carefully, using individual properties of matrix multiplication and inverses.