MATH
HW2

# HW2 - Math 104 Fall 2009 Homework 2 Due Wednesday October 7...

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Math 104 Fall 2009 Homework 2 Due Wednesday, October 7, 2009 1. Let A and B be square, invertible matrices. Prove that the inverse of AB is B - 1 A - 1 . 2. Exercise 1.3, Chapter 1 of Trefethen-Bau. 3. (a) Find a square matrix A , whose entries are not all zeros, such that A 2 = 0. (The matrix A 2 is of course AA .) (b) Exhibit a nonzero vector that belongs to the nullspace of the matrix you just constructed. (c) In general, prove that if a matrix
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Unformatted text preview: B satisﬁes B 2 = 0, then it cannot be invertible. 4. If u and v are two vectors such that k u k = 3 and k v k = 5, (a) what are the smallest and largest values of k u-v k ? (b) and what are the smallest and largest values of h u,v i ? 5. Exercise 2.1, Chapter 2 of Trefethen-Bau. [A diagonal matrix is a matrix whose oﬀ-diagonal elements ( i 6 = j ) are zero.] 1...
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