6.1 (2 points) Compute nice(A ) for the matrix A = NJ 62 (3 points) True or False: If A is a 2 x 2 matrix with we(A) = 1, then def (A) = 1,0 or -1. 63 (2 BONUS points) Prove part 2 of the first Theorem above, namely that for any square matrix A and real number k, we have we(KA) = [k| - me(A).6 (5 points, plus 2 BONUS points) Read the following carefully, and then answer the questions that follow. In the latest tutorial worksheet, you were introduced to the notions of the "thickness" and "depth" of a matrix. Here we will define a similar idea, called the "weight" of a matrix, and explore it a bit: Given an n x n matrix A, we define the weight of A, denoted as we( A), to be: we( A) = Definition 15i,jen In other words, it is the square root of the sum of the squares of all entries in A. Let A = Example 1/2 0 Then we( A) = v1+ (-7)- + (1/2)- +0 = v50.25 = 7.09. Here are some facts about weight that may be useful. Aside from the BONUS question, where you are asked to prove one of them, you may assume they are true. For any square matrices A and B and real number A: 1. we(A) 2 0 and we( A) = 0 if and only if A is the zero matrix. Theorem 2. we(KA) = [k| - we( A) 3. we( AB)