Problem 4. Find the characteristic polynomials of the following matrices. (L 12 6-11 (2.)[-2021 3 0...
find the eigen space of 4a and 4c Find the characteristic equations of the following matrices 4. (a) 「 4 0 1 -2 1 0 -2 0 1 (b) [3 0-5 1 1-2 11 1-2 0 (c) 19 5 -4 (d) -1 0 11 -1 3 0 -4 13 1 (e) 5 0 11 ind bases for the eigenspaces of the matrices in Exercise 4 6. Find the characteristic equations of the following matrices 4. (a) 「 4 0 1...
(a) Reduce the following matrices to diagonal form and find a g-inverse of each 120-11 4 5 6 2 2 3 -1 A=158 O 11 and B-1084 7 1o-2 3 21 6 (5+5 (b) () For any n x I vector a 0, show that a (ii) Find the g-inverse of the vector a, where a' = [1 a'a 5 2] 3 1 (a) Reduce the following matrices to diagonal form and find a g-inverse of each 120-11 4 5...
ex 1.3 Ex. 1.3. For the following 3 x 3 matrices find their characteristic equations, their eigenvalues and the corresponding eigenvectors [2 2 11 4 0 1 5 0 1 5 1 (a)2 1 0; (b) 3 1(d) 1(c) 1 1 2 1 1 0 -7 1 -2 0 1 -2 1 2 2 Ex. 1.3. For the following 3 x 3 matrices find their characteristic equations, their eigenvalues and the corresponding eigenvectors [2 2 11 4 0 1 5...
Problem: A+C=? Use the matrices defined below for the following set of problems. [1 0 6 [2 3 [2 31 A = 5 7 2 3] B = 5 7 [2 3 8 1 01 C 5 7 F 0 2 3 E = 0 1 5 7 12 6 9 4 0 0 II Use the matrices defined below for the following set of problems. [1 0 6 [2 3 [2 31 A = 5 7 2 3] B...
0 4 -1 1 5. Given, A--2 6 -11 L-2 8-3 1 has the characteristic polynomial p(λ)-(x + 2) (z-2)2(z-1) Find the corresponding eigenvector for each eigenvalue 0 4 -1 1 5. Given, A--2 6 -11 L-2 8-3 1 has the characteristic polynomial p(λ)-(x + 2) (z-2)2(z-1) Find the corresponding eigenvector for each eigenvalue
Question 4: 4. Show that the following polynomials form a basis for P3 1 - x, 1-x2 1 +x _X 5. Show that the following matrices form a basis for M22 -8 1 0 3 12 -6 -4 2 _ 13. Find the coordinate vector of v relative to the basis S = {v1, V2, V3} for R3 (a) v (2, -1 3); vi = (1,0, 0), v2 = (2, 2, 0) Vз — (3, 3, 3) (b) v (5,...
Let A, B,C be matrices with the singular value decompositions 1. A-(4/5-3/5) ( 0 0 1 0 2 0 0 0 100 1叭-1/2 V3/2 2. B=11 00110 2 113 0 01 0 TO V3 V3 V3 a. Find the characteristic polynomials and eigenvalues of AA" and ATA, BBT and BTB, CCTand CTC. b. Find the largest possible value of IlAvILBvICvll, for the corresponding unit vectors v. c. Sketch the image, under A, B, C, of the unit sphere in the...
Find determinants of the following matrices: 1 5 7 -1 3 2 A= 3 2 8 B= 6 -2 3 C= 6 1 9 7 10 0 13 4 1 0 4 1 -7 2 3 -4 3 D= 4 12 -3 -9 2 6 7 8
* Problem #4: Pivot the following matrix, 1-4 12 -4 -20 2 1 -2 -2 2 1 2 4 Thira about the entry 011: ſi -3 1 5 1 [i -3 1 5 [i -3 1 51 [1 -3 1 5 1 (A) O 7 -4 -12 (B) O 7 -3 -12 (C) 0 7 -3 -9 ( D O 7 -4 -11 Lo 7 0 -6] LO 7 3 -3 ] [O 7 0 -3] LO 8 0 -6]...
1. Find the Jordan canonical forms of the following matrices 0 0 -1 (c) 7 6-3 (b) 2 3 2 1 0 4 0 1 -3 -10-8-6-4 0 -3 1 2 0-1 0 0 0 (d) 2 2 21-1 2 (e) 0-2-5-3 -2 0 6 85 4 0 -5 3-3 -2-3 4 1. Find the Jordan canonical forms of the following matrices 0 0 -1 (c) 7 6-3 (b) 2 3 2 1 0 4 0 1 -3 -10-8-6-4 0...