Asn 3 - Math 473/573 Assignment 3 Due Tuesday February 9...

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Math 473/573 - Assignment 3 Due: Tuesday, February 9. Nothing accepted after Thursday, February 11. This is worth 20 points. 10% points off for being late. Please work by yourself. See me if you need help. 1. Let x = and p = ( p 1 , p a. (2 points) What is || x || ? Find p such that px = || x || and || p || b. (2 points) What is || x || 1 ? Find p such that px = || x || 1 and || p || c. (2 points) What is || x || 2 ? Find p such that px = || x || 2 and || p || 3. Let A = . In this problem assume that the norms are norms. a. (1 points) What is || A ||? b. (1 points) Find a vector x such that || x || = 1 and || Ax || = || c. (1 points) What is || A -1 ||? d. (1 points) Find a vector v such that || v || = 1 and || A -1 v || = || A -1 3. Read section 1.7.1 - Nodal Analysis of the online notes. Consider the circuit in Figure 1.5 on page 20 of the text ( Fundamentals of Matrix Computations , 3 rd ed. by David Watkins). The x k in that diagram are the potentials (or nodal voltages) at each of the nodes. They are denoted by v k in the online notes in section 1.7.1. Suppose the lines are numbered so that Line 1 goes from node 1 to node 2 Line 2 goes from node 2 to node 3 2 ). 1 = 1. = 1. 2 = 1. A ||. ||.

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