Homework Answers
(1 point) The matrix -1 -1 01 A = -16 0 Lk 0 has three distinct...
(1 point) The matrix -1 -1 01 A = -16 0 Lk 0 has three distinct real eigenvalues if and only if -17.036 <k< 29.184
Consider the matrix: 15 9 13 2 6 10 14 3 7 11 15 4 8 12 16 a- Find the eigenvectors of this matri...
Consider the matrix: 15 9 13 2 6 10 14 3 7 11 15 4 8 12 16 a- Find the eigenvectors of this matrix and their corresponding eigenvalues. b-Indicate if there are any degeneracy, and if so, change only one element of this matrix to remove this degeneracy (of course you need to recompute the eigenvalues to show that the degeneracy was lifted). Write a Mathematica program to calculate the roots of the following function f(x) = 0.5*e*-5*x+2 using...
1.) Write a Boolean equation in sum-of-products (SoP) canonical form for each of the truth tables:...
1.) Write a Boolean equation in sum-of-products (SoP) canonical form for each of the truth tables: A B C DY 0 0 00 1 0 0 01 0 0 0 01 0 0 11 0 1000 0 1 01 0 0 1 1 0 1 0 1 1 1 0 1 0 0 1 1 0 101 0 1 11 1 0 0 1 1 0 1 0 1 1 01 1 1 10 0 0 1 1 0 100...
4. (15 pts Consider the following direction fields IV VI (5 pts)Which of the direction fields corresponds to the system x -Ax, where A is a 2x2 matrix with eigenvalues λ,--1 and λ2-2 and correspondin...
4. (15 pts Consider the following direction fields IV VI (5 pts)Which of the direction fields corresponds to the system x -Ax, where A is a 2x2 matrix with eigenvalues λ,--1 and λ2-2 and corresponding eigenvectors vand v- 1? a. is a 2x2 matrix with repeated eigenvalue λ = 0 with defect 1 (has only one linearly independent eigenvector, not two.) and corresponding eigenvector vi- 13 (5 pts) Which of the direction fields corresponds to the system x -Cx, where...
Show that the matrix is not diagonalizable. 2 43 0 21 0 03 STEP 1: Use...
Show that the matrix is not diagonalizable. 2 43 0 21 0 03 STEP 1: Use the fact that the matrix is triangular to write down the eigenvalues. (Enter your answers from smallest to largest.) -- STEP 2: Find the eigenvectors x, and X corresponding to d, and 12, respectively, STEP 3: Since the matrix does not have Select linearly independent eigenvectors, you can conclude that the matrix is not diagonalizable.
2. (-16 Points) DETAILS CHENEYLINALG2 6.1.017. 0/2 Submissions Used 9 Let A - Find the characteristic...
2. (-16 Points) DETAILS CHENEYLINALG2 6.1.017. 0/2 Submissions Used 9 Let A - Find the characteristic polynomial. 11 Det(A - AI) - Find the eigenvalues and eigenvectors for each eigenvalue. (Order your answers from smallest to largest eigenvalue.) 21 has eigenspace span 12 has eigenspace span Find a matrix P such that p-'AP is a diagonal matrix. P
Linear Algebra Problem! Problem 4 (Jordan Canonical Form). Let A be a matrix in C6,6 whose...
Linear Algebra Problem!
Problem 4 (Jordan Canonical Form). Let A be a matrix in C6,6 whose Jordan Canonical form is given by ON OON JODODD JODOC JOOD 000000 E C6,6 ] O O O O O As we gradually give you more and more information about A below, fill in the blanks in J (and explain how you know the filled in values are correct). You may choose to order the Jordan blocks however you wish. Note: during the interview,...
(23). (15 Marks). Suppose A has eigenvalues 11 = 3, 12 = 1, 13 = 0)...
(23). (15 Marks). Suppose A has eigenvalues 11 = 3, 12 = 1, 13 = 0) with corresponding eigenvectors 0 0 2 = [1] 12 8) 23 = (a) (5 points). How do you know that the third column of A contains all zeros? (b) (10 points). Find the matrix A.
I need it in the Jordan Canonical Form. The solution should look like: (8 points) Solve...
I need it in the Jordan Canonical Form. The solution should look
like:
(8 points) Solve the system of differential equations x'(t) = [-2 0 1 2 -3 2 -37 1 -4 x(t), x(0) = The only eigenvalue of this matrix is -3, a triple root. You must explicitly find any matrix involved, with the exception of any matrix inverses (in the same way that the solutions were done in class). Also, your answer cannot involve the imaginary number i....
13-15 please! 13. a 14. 15. 0 Find the eigenspaces of A = 0 1 -1...
13-15 please!
13. a 14. 15. 0 Find the eigenspaces of A = 0 1 -1 Then diagonalize A if you can. LO 0 1 b Determine values a, b, c for matrix A = 0 -2 c to be diagonalizable. LO 0 1) For nxn matrix A and B, true or false? a. A is diagonalizable if the sum of geometric multiplicities of the eigenvalues is n b. If A is invertible, the only real eigenvalues are 1 and...
(1 point) The matrix -1 -1 01 A = -16 0 Lk 0 has three distinct real eigenvalues if and only if -17.036 <k< 29.184
Consider the matrix: 15 9 13 2 6 10 14 3 7 11 15 4 8 12 16 a- Find the eigenvectors of this matrix and their corresponding eigenvalues. b-Indicate if there are any degeneracy, and if so, change only one element of this matrix to remove this degeneracy (of course you need to recompute the eigenvalues to show that the degeneracy was lifted). Write a Mathematica program to calculate the roots of the following function f(x) = 0.5*e*-5*x+2 using...
1.) Write a Boolean equation in sum-of-products (SoP) canonical form for each of the truth tables: A B C DY 0 0 00 1 0 0 01 0 0 0 01 0 0 11 0 1000 0 1 01 0 0 1 1 0 1 0 1 1 1 0 1 0 0 1 1 0 101 0 1 11 1 0 0 1 1 0 1 0 1 1 01 1 1 10 0 0 1 1 0 100...
4. (15 pts Consider the following direction fields IV VI (5 pts)Which of the direction fields corresponds to the system x -Ax, where A is a 2x2 matrix with eigenvalues λ,--1 and λ2-2 and corresponding eigenvectors vand v- 1? a. is a 2x2 matrix with repeated eigenvalue λ = 0 with defect 1 (has only one linearly independent eigenvector, not two.) and corresponding eigenvector vi- 13 (5 pts) Which of the direction fields corresponds to the system x -Cx, where...
Show that the matrix is not diagonalizable. 2 43 0 21 0 03 STEP 1: Use the fact that the matrix is triangular to write down the eigenvalues. (Enter your answers from smallest to largest.) -- STEP 2: Find the eigenvectors x, and X corresponding to d, and 12, respectively, STEP 3: Since the matrix does not have Select linearly independent eigenvectors, you can conclude that the matrix is not diagonalizable.
2. (-16 Points) DETAILS CHENEYLINALG2 6.1.017. 0/2 Submissions Used 9 Let A - Find the characteristic polynomial. 11 Det(A - AI) - Find the eigenvalues and eigenvectors for each eigenvalue. (Order your answers from smallest to largest eigenvalue.) 21 has eigenspace span 12 has eigenspace span Find a matrix P such that p-'AP is a diagonal matrix. P
Linear Algebra Problem!
Problem 4 (Jordan Canonical Form). Let A be a matrix in C6,6 whose Jordan Canonical form is given by ON OON JODODD JODOC JOOD 000000 E C6,6 ] O O O O O As we gradually give you more and more information about A below, fill in the blanks in J (and explain how you know the filled in values are correct). You may choose to order the Jordan blocks however you wish. Note: during the interview,...
(23). (15 Marks). Suppose A has eigenvalues 11 = 3, 12 = 1, 13 = 0) with corresponding eigenvectors 0 0 2 = [1] 12 8) 23 = (a) (5 points). How do you know that the third column of A contains all zeros? (b) (10 points). Find the matrix A.
I need it in the Jordan Canonical Form. The solution should look
like:
(8 points) Solve the system of differential equations x'(t) = [-2 0 1 2 -3 2 -37 1 -4 x(t), x(0) = The only eigenvalue of this matrix is -3, a triple root. You must explicitly find any matrix involved, with the exception of any matrix inverses (in the same way that the solutions were done in class). Also, your answer cannot involve the imaginary number i....
13-15 please!
13. a 14. 15. 0 Find the eigenspaces of A = 0 1 -1 Then diagonalize A if you can. LO 0 1 b Determine values a, b, c for matrix A = 0 -2 c to be diagonalizable. LO 0 1) For nxn matrix A and B, true or false? a. A is diagonalizable if the sum of geometric multiplicities of the eigenvalues is n b. If A is invertible, the only real eigenvalues are 1 and...
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