ind bases for the eigenspaces of the matrices in Exercise 4 6.
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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...
ex 1.3 Ex. 1.3. For the following 3 x 3 matrices find their characteristic equations, their eigenvalues and the corresp...
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 4. Find the characteristic polynomials of the following matrices. (L 12 6-11 (2.)[-2021 3 0...
Problem 4. Find the characteristic polynomials of the following matrices. (L 12 6-11 (2.)[-2021 3 0 0 0 0 -5 1 000 ) 3 s 0 0 o 0 7 2 1(0 -4 1 9 2 3 (3)1 1 0-I (1.) 2 3( (2.) 5 3 2
3. A coupled system of differential equations is expressed in matrix form. Using the matrices technique,...
3. A coupled system of differential equations is expressed in matrix form. Using the matrices technique, determine the following. 1 0 0 -24 + a) The characteristic equation. b) The 2 Eigen values. c) The 2 Eigen vectors. d) The homogeneous solution (complementary function). e) The non-homogeneous solution (particular.function). f) The full solutions expressed for X1 and X2. [5 marks] [5 marks] [6 marks] [3 marks] (12 marks] [2 marks] CS Scanned with CamScanner Q3 Total [33 marks] END OF...
1. Find the eigenvalues for the following matrices and bases for their corresponding eigenspaces. -28 10...
1. Find the eigenvalues for the following matrices and bases for their corresponding eigenspaces. -28 10 (a) -75 27 -3 -4 6 (b) 8 12-18 4 5 -7 -17 5 5 (c) -40 13 10 -20 5 8
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. 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...
15. Use the characteristic equation to find the real eigenvalues of the following matrices. (a) [...
15. Use the characteristic equation to find the real eigenvalues of the following matrices. (a) [ ] 6 (b) | 9 -9 -6 -9 6 -6 3 1 16. Diagonalize the following matrices if possible. (If not possible explain why not)Then compute A2. (Use the diagonal matrix to do the computation if A was diagonalizable) One of the Eigen-values is provided to get you started. A= 10 -1 15 3 -9 2=4 -2 10)
(4) (15 marks) Repeat the Question 2 for the following matrices -3 4 0] 0 0...
(4) (15 marks) Repeat the Question 2 for the following matrices -3 4 0] 0 0 A -2 30 B 0 -1 0 -8 8 1 0 0 1 ū= 10 = > 3 (I) (2 mark) Find the characteristic polynomial of matrix A. (II) (1 mark) Find eigenvalues of the matrix A. III) (2 mark) Find a basis for the eigenspaces of matrix A. IV) (1 mark) What is the algebraic and geometric multiplicities of its eigenvalues. (V) (2...
5. Consider the matrix A-1-6-7-3 Hint: The characteristic polynomial of A is p(λ ) =-(-2)0+ 1)2....
5. Consider the matrix A-1-6-7-3 Hint: The characteristic polynomial of A is p(λ ) =-(-2)0+ 1)2. (a) Find the eigenvalues of A and bases for the corresponding eigenspaces. (b) Determine the geometric and algebraic multiplicities of each eigenvalue and whether A is diagonalizable or not. If it is, give a diagonal matrix D and an invertible matrix S such that A-SDS-1. If it's not, say why not.
(1 point) Find a basis for the column space of 0 A = -1 2 3...
(1 point) Find a basis for the column space of 0 A = -1 2 3 3 - 1 2 0 - 1 -4 0 2 Basis = (1 point) Find the dimensions of the following vector spaces. (a) The vector space RS 25x4 (b) The vector space R? (c) The vector space of 6 x 6 matrices with trace 0 (d) The vector space of all diagonal 6 x 6 matrices (e) The vector space P3[x] of polynomials with...
1. Find a basis for the null space and row space of 1-13 (a) A 5-4 -4 7 -6 2 2 0 3 (b) A544 7 -6 2
1. Find a basis for the null space and row space of 1-13 (a) A 5-4 -4 7 -6 2 2 0 3 (b) A544 7 -6 2
1. Find a basis for the null space and row space of 1-13 (a) A 5-4 -4 7 -6 2 2 0 3 (b) A544 7 -6 2
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 4. Find the characteristic polynomials of the following matrices. (L 12 6-11 (2.)[-2021 3 0 0 0 0 -5 1 000 ) 3 s 0 0 o 0 7 2 1(0 -4 1 9 2 3 (3)1 1 0-I (1.) 2 3( (2.) 5 3 2
3. A coupled system of differential equations is expressed in matrix form. Using the matrices technique, determine the following. 1 0 0 -24 + a) The characteristic equation. b) The 2 Eigen values. c) The 2 Eigen vectors. d) The homogeneous solution (complementary function). e) The non-homogeneous solution (particular.function). f) The full solutions expressed for X1 and X2. [5 marks] [5 marks] [6 marks] [3 marks] (12 marks] [2 marks] CS Scanned with CamScanner Q3 Total [33 marks] END OF...
1. Find the eigenvalues for the following matrices and bases for their corresponding eigenspaces. -28 10 (a) -75 27 -3 -4 6 (b) 8 12-18 4 5 -7 -17 5 5 (c) -40 13 10 -20 5 8
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...
15. Use the characteristic equation to find the real eigenvalues of the following matrices. (a) [ ] 6 (b) | 9 -9 -6 -9 6 -6 3 1 16. Diagonalize the following matrices if possible. (If not possible explain why not)Then compute A2. (Use the diagonal matrix to do the computation if A was diagonalizable) One of the Eigen-values is provided to get you started. A= 10 -1 15 3 -9 2=4 -2 10)
(4) (15 marks) Repeat the Question 2 for the following matrices -3 4 0] 0 0 A -2 30 B 0 -1 0 -8 8 1 0 0 1 ū= 10 = > 3 (I) (2 mark) Find the characteristic polynomial of matrix A. (II) (1 mark) Find eigenvalues of the matrix A. III) (2 mark) Find a basis for the eigenspaces of matrix A. IV) (1 mark) What is the algebraic and geometric multiplicities of its eigenvalues. (V) (2...
5. Consider the matrix A-1-6-7-3 Hint: The characteristic polynomial of A is p(λ ) =-(-2)0+ 1)2. (a) Find the eigenvalues of A and bases for the corresponding eigenspaces. (b) Determine the geometric and algebraic multiplicities of each eigenvalue and whether A is diagonalizable or not. If it is, give a diagonal matrix D and an invertible matrix S such that A-SDS-1. If it's not, say why not.
(1 point) Find a basis for the column space of 0 A = -1 2 3 3 - 1 2 0 - 1 -4 0 2 Basis = (1 point) Find the dimensions of the following vector spaces. (a) The vector space RS 25x4 (b) The vector space R? (c) The vector space of 6 x 6 matrices with trace 0 (d) The vector space of all diagonal 6 x 6 matrices (e) The vector space P3[x] of polynomials with...
1. Find a basis for the null space and row space of 1-13 (a) A 5-4 -4 7 -6 2 2 0 3 (b) A544 7 -6 2
1. Find a basis for the null space and row space of 1-13 (a) A 5-4 -4 7 -6 2 2 0 3 (b) A544 7 -6 2
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