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- © consider the companion form matrix a) b) show its characteristic polynomial is Pa ()...
Let p(x) be the polynomial The companion matrix of p(x) is the n x n matrix...
Let p(x) be the polynomial The companion matrix of p(x) is the n x n matrix 1 1 n-2 .. -a-a0 cp) = 10 1 0 Find the companion matrix of p(x) - x3 + 5x2 - 2x 15 and then find the characteristic polynomial of C(p). C(p) det(C(p) Xr)-
1. Consider the matrix (a) Find the characteristic polynomial and eigenvalues of A (b) Find a...
1. Consider the matrix (a) Find the characteristic polynomial and eigenvalues of A (b) Find a basis for the eigenspace corresponding to each eigenvalue of A. (c) Find a diagonalization of A. That is, find an invertible matrix P and a diagonal matrix such that A - POP! (d) Use your diagonalization of A to compute A'. Simplify your answer.
(1 point) Find the characteristic polynomial of the matrix 5 -5 A = 0 [ 5...
(1 point) Find the characteristic polynomial of the matrix 5 -5 A = 0 [ 5 -5 -2 5 0] 4. 0] p(x) = (1 point) Find the eigenvalues of the matrix [ 23 C = -9 1-9 -18 14 9 72 7 -36 : -31] The eigenvalues are (Enter your answers as a comma separated list. The list you enter should have repeated items if there are eigenvalues with multiplicity greater than one.) (1 point) Given that vi =...
1. Consider the matrix A= 1 3 -3 (a) Find the characteristic polynomial and eigenvalues of...
1. Consider the matrix A= 1 3 -3 (a) Find the characteristic polynomial and eigenvalues of A. (b) Find a basis for the eigenspace corresponding to each eigenvalue of A.
Problem 1: Consider the matrix 3 -2 -11 A = -1 2 -1 |-1 -2 3...
Problem 1: Consider the matrix 3 -2 -11 A = -1 2 -1 |-1 -2 3 a) Find the characteristic polynomial of A and show that A has an eigenvalue at zero. Find the other two eigenvalues of A. b) Find an eigenvector of A corresponding to all eigenvalue. c) Can you diagonalize this matrix?
Q5. Consider the square matrix A = (a) Show that the characteristic polynomial of A is:...
Q5. Consider the square matrix A = (a) Show that the characteristic polynomial of A is: p(A) = 12 - 82-3. (5 pts) (b) Compute the matrix B-A? - SA - 3/2 (5 pts) (c) Show that A? - 8A - 3/2 for the given matrix A. (5 pts) (d) Is it possible to use the equation A? - 8A = 37, to find the inverse of the given matrix A? (Justify your answer) 5 pts)
Q5. Consider the square matrix A = [] (a) Show that the characteristic polynomial of A...
Q5. Consider the square matrix A = [] (a) Show that the characteristic polynomial of A is: p(4) = 12 - 91 - 2. (5 pts) (b) Compute the matrix B= AP-9A - 212. (5 pts) (e) Show that A² - 9A = 21, for the given matrix A. (5 pts) (d) Is it possible to use the equation A? - 9A = 212 to find the inverse of the given matrix A? (Justify your answer) (5 pts)
Q5. Consider the square matrix A 4 -3 2 (a) Show that the characteristic polynomial of...
Q5. Consider the square matrix A 4 -3 2 (a) Show that the characteristic polynomial of A is: p(x) = 12 – 61 – 7. (b) Compute the matrix B= A2 – 6A – 712. (c) Show that A² – 6A = 712 for the given matrix A. (d) Is it possible to use the equation A2 – 6A = 712 to find the inverse of the given matrix A? (Justify your answer)
Q5. Consider the square matrix A - 6 4 3 (a) Show that the characteristic polynomial...
Q5. Consider the square matrix A - 6 4 3 (a) Show that the characteristic polynomial of A# (X) = x-91-2. (6 pts) (b) Compute the matrix B-A 9A 21. (5 pts) (c) Show that A2 9A-21, for the given matrix A. (5 pts) (d) Is it possible to use the equation A? (Justify your answer) (5 pts) 9A 21, to incl the inverse of the given matrix A
Question 3 Consider the matrix A. (rowt:10, 2, -1];row2 2,3,-2): row:(-1, -2,01). 1. Show that V2-vector...
Question 3 Consider the matrix A. (rowt:10, 2, -1];row2 2,3,-2): row:(-1, -2,01). 1. Show that V2-vector column [-2. 1. Oj is an eigenvector for A and find its corresponding eigenvalue L1. 2. Diagonalizable A given that its characteristic polynomial is P(L) = -_LA3) + 3"(L^2)+ 9*L+5.
Let p(x) be the polynomial The companion matrix of p(x) is the n x n matrix 1 1 n-2 .. -a-a0 cp) = 10 1 0 Find the companion matrix of p(x) - x3 + 5x2 - 2x 15 and then find the characteristic polynomial of C(p). C(p) det(C(p) Xr)-
1. Consider the matrix (a) Find the characteristic polynomial and eigenvalues of A (b) Find a basis for the eigenspace corresponding to each eigenvalue of A. (c) Find a diagonalization of A. That is, find an invertible matrix P and a diagonal matrix such that A - POP! (d) Use your diagonalization of A to compute A'. Simplify your answer.
(1 point) Find the characteristic polynomial of the matrix 5 -5 A = 0 [ 5 -5 -2 5 0] 4. 0] p(x) = (1 point) Find the eigenvalues of the matrix [ 23 C = -9 1-9 -18 14 9 72 7 -36 : -31] The eigenvalues are (Enter your answers as a comma separated list. The list you enter should have repeated items if there are eigenvalues with multiplicity greater than one.) (1 point) Given that vi =...
1. Consider the matrix A= 1 3 -3 (a) Find the characteristic polynomial and eigenvalues of A. (b) Find a basis for the eigenspace corresponding to each eigenvalue of A.
Problem 1: Consider the matrix 3 -2 -11 A = -1 2 -1 |-1 -2 3 a) Find the characteristic polynomial of A and show that A has an eigenvalue at zero. Find the other two eigenvalues of A. b) Find an eigenvector of A corresponding to all eigenvalue. c) Can you diagonalize this matrix?
Q5. Consider the square matrix A = (a) Show that the characteristic polynomial of A is: p(A) = 12 - 82-3. (5 pts) (b) Compute the matrix B-A? - SA - 3/2 (5 pts) (c) Show that A? - 8A - 3/2 for the given matrix A. (5 pts) (d) Is it possible to use the equation A? - 8A = 37, to find the inverse of the given matrix A? (Justify your answer) 5 pts)
Q5. Consider the square matrix A = [] (a) Show that the characteristic polynomial of A is: p(4) = 12 - 91 - 2. (5 pts) (b) Compute the matrix B= AP-9A - 212. (5 pts) (e) Show that A² - 9A = 21, for the given matrix A. (5 pts) (d) Is it possible to use the equation A? - 9A = 212 to find the inverse of the given matrix A? (Justify your answer) (5 pts)
Q5. Consider the square matrix A 4 -3 2 (a) Show that the characteristic polynomial of A is: p(x) = 12 – 61 – 7. (b) Compute the matrix B= A2 – 6A – 712. (c) Show that A² – 6A = 712 for the given matrix A. (d) Is it possible to use the equation A2 – 6A = 712 to find the inverse of the given matrix A? (Justify your answer)
Q5. Consider the square matrix A - 6 4 3 (a) Show that the characteristic polynomial of A# (X) = x-91-2. (6 pts) (b) Compute the matrix B-A 9A 21. (5 pts) (c) Show that A2 9A-21, for the given matrix A. (5 pts) (d) Is it possible to use the equation A? (Justify your answer) (5 pts) 9A 21, to incl the inverse of the given matrix A
Question 3 Consider the matrix A. (rowt:10, 2, -1];row2 2,3,-2): row:(-1, -2,01). 1. Show that V2-vector column [-2. 1. Oj is an eigenvector for A and find its corresponding eigenvalue L1. 2. Diagonalizable A given that its characteristic polynomial is P(L) = -_LA3) + 3"(L^2)+ 9*L+5.
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