2. Let u eRm and ve Rn be two non-zero vectors, in other words at least one component of the vectors is non-zero. Let A=

[answerhappygod]

2 Let U Erm And Ve Rn Be Two Non Zero Vectors In Other Words At Least One Component Of The Vectors Is Non Zero Let A 1 (65.04 KiB) Viewed 27 times

2. Let u eRm and ve Rn be two non-zero vectors, in other words at least one component of the vectors is non-zero. Let A= = uyT ERmXn (a) Suppose ||u|l2 = 1 and || vll2 = 1. Show that the Frobenius norm of A is equal to 1. (b) Consider the case where m= 3 and n = 2, i.e., = u = u1 U2 U3 V = Vi U2 To help simplify your work in the following subproblems you may assume ui #0 and vi 70. i. Derive a basis for the range of A using Gaussian elimination. What is the rank of A? ii. Derive a basis for the null space of A using Gaussian elimination. (c) Now consider the general case where m and n are any positive integers. To help simplify your work in the following subproblems you may assume 1 + 0 and vi 70. i. Generalize your work from b.i to derive a basis for the range of A. What is the rank of A? ii. Generalize your work from b.ii to derive a basis for the null space of A.