Question 01 [20 Points] 1. Use the following matrix to answer the questions below. [1 2 3 1 -2 A= 2 4 6 B= - 1 1 -2 5 10

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Question 01 20 Points 1 Use The Following Matrix To Answer The Questions Below 1 2 3 1 2 A 2 4 6 B 1 1 2 5 10 1 (127.3 KiB) Viewed 39 times

PLEASE answer "all" questions with 100% accuracy asap, need solutions before right nowsubmission time almost up
Question 01 [20 Points] 1. Use the following matrix to answer the questions below. [1 2 3 1 -2 A= 2 4 6 B= - 1 1 -2 5 10 15 - 1 2 a) Is AB = 0 [5 Points] b) Find a vector x such that the following equation Ax = 0. [5 Points] 2. Let [3 1 11 A= 1 0 2 1 2 0 . a) The eigenvalues of A are 1, 4, -2. Find the normalized eigenvectors and use them as columns in an orthogonal matrix C. [5 Points] b) Show that C' AC = D where D is a diagonal with eigenvalues of A on the diagonal. 1 2 QUESTION 3 (25 Points] Use the table below to answer the following questions. Subject No. 1 2 3 4 Y2 35 5 Yi 51 32 61 30 64 Y3 41 33 11 57 33 Y4 28 18 48 39 55 Y5 17 47 37 58 10 45 24 25 5 1. Find the mean vector. [5 Points] 2. Find Z1, Z2 and 23, the linear combinations using the given Points) 3. Find the covariance matrix. [9 Points) 4. How would you calculate the correlation matrix, give an example. [5 Points]