Homework Answers
Answer 7,8,9 1-11-1)--[-13.-(41-44)--:-- 3 1 0 0 -1 0 5 4 2-3 0 0 0 6....
Answer 7,8,9
1-11-1)--[-13.-(41-44)--:-- 3 1 0 0 -1 0 5 4 2-3 0 0 0 6. Consider the matrix A, above. Use diagonalization to evaluate A. 7. Consider the matrix B, above. Find a diagonal matrix D, and invertible matrix P, such that BPDP-1 8. Consider the matrix C, above. Find a diagonal matrix D, and invertible matrix P, such that C = PDP-1. If this is not possible, thus the matrix is not diagonalizable, explain why. 9. Consider the...
LA class!! 1. Find a diagonlizing matrix P for the matrix A and write A in...
LA class!!
1. Find a diagonlizing matrix P for the matrix A and write A in the form A = PDP-1 where D is a diagonal matrix. AE 5 -6 3 3 -4 3 0 0 2 Also, use the diagonalization of A to compute A8, A-8, and eA.
5.3: Diagonalization Find the diagonal matrix D and invertible matrix P such that A- PDp-1 if pos...
I
5.3: Diagonalization Find the diagonal matrix D and invertible matrix P such that A- PDp-1 if possible. If it is not possibl which eigenspace(s) are to blame. e, eosplain A-1 2 1 3 -1 A 1 1 1 5 0 3 A- 0 2 0 し406
5.3: Diagonalization Find the diagonal matrix D and invertible matrix P such that A- PDp-1 if possible. If it is not possibl which eigenspace(s) are to blame. e, eosplain A-1 2 1 3...
4. Consider the following matrix [1 0 -27 A=000 L-2 0 4] (a) (3 points) Find...
4. Consider the following matrix [1 0 -27 A=000 L-2 0 4] (a) (3 points) Find the characteristic polynomial of A. (b) (4 points) Find the eigenvalues of A. Give the algebraic multiplicity of each eigenvalue (c) (8 points) Find the eigenvectors corresponding to the eigenvalues found in part (b). (d) (4 points) Give a diagonal matrix D and an invertible matrix P such that A = PDP-1 (e) (6 points) Compute P-and verify that A= PDP- (show your steps).
Next Problem (1 point) Suppose 7 A 8 -5 Find an invertible matrix P and a...
Next Problem (1 point) Suppose 7 A 8 -5 Find an invertible matrix P and a diagonal matrix D so that A = PDP-1. Use your answer to find an expression for AⓇ in terms of P, a power of D, and P-1 in that order. -] 1/2 1 -1 0 -2 2 A6 1 1 0 3 2 -1 Note: In order to get credit for this problem all answers must be correct.
Name: 1. Find a diagonlizing matrix P for the matrix A and write A in the...
Name: 1. Find a diagonlizing matrix P for the matrix A and write A in the form A = PDP-1 where D is a diagonal matrix. 55 -6 37 A = 3 -4 31 To o 2 Also, use the diagonalization of A to compute AS, A-8, and e^. 2. Find the QR-decomposition of the following matrix: [ 1 2 2] A= 11 2 2 1 0 21 1-1 0 2] 3. Use the Gram-Schmidt process to construct an orthogonal...
Problem 8. a) Find the determinant det (A) for the matrix [1 -3 41 A 2...
Problem 8. a) Find the determinant det (A) for the matrix [1 -3 41 A 2 0 -1 1 b) Decide whether the matrix A has an inverse. If the inverse matrix A-1 exists, find its determinant det(A-1).
Diagonzalize the matrix A. if possible. That is, find an invertible matrix P and 1 3...
Diagonzalize the matrix A.
if possible. That is, find an invertible matrix P and 1 3 3 Diagonalize the matrix A= - 3 - 5 -3 3 3 a diagonal matrix D such that A = PDP-1. 1
Find a 3 × 3 matrix A with eigenvectors v1 = 1 2 3...
Find a 3 × 3 matrix A with eigenvectors v1
= 1 2 3 with λ = 1, v2 = 0 −1 1 with λ = 2 and v3 =
1 1 1 with λ = 10. (Hint: A must be diagonalizable, A = P
DP −1 . Figure out P and D, then compute A directly.)
(6) Find a 3 x 3 matrix A with eigenvectors V1...
Find the eigenvalues of the given matrix. [-14 -6 36 16 1) A) -2.-4 B)-4 C)-2...
Find the eigenvalues of the given matrix. [-14 -6 36 16 1) A) -2.-4 B)-4 C)-2 D) -24 The characteristic polynomial of a 5 5 matrix is given below. Find the eigenvalues and their multiplicities 2) A5 - 24A4-189A3-486A2 2) A) 0 (multiplicity 2),-9 (multiplicity 2),-6 (multiplicity 1) B) 0 (multiplicity 1),9 (multiplicity 3), 6 (multiplicity ) C) 0 (multiplicity 2),9 (multiplicity 2),6 (multiplicity 1) D) 0 (multiplicity 2),-9 (multiplicity 2),6 (multiplicity 1) Diagonalize A- PDP-1 the matrix A, if...
Answer 7,8,9
1-11-1)--[-13.-(41-44)--:-- 3 1 0 0 -1 0 5 4 2-3 0 0 0 6. Consider the matrix A, above. Use diagonalization to evaluate A. 7. Consider the matrix B, above. Find a diagonal matrix D, and invertible matrix P, such that BPDP-1 8. Consider the matrix C, above. Find a diagonal matrix D, and invertible matrix P, such that C = PDP-1. If this is not possible, thus the matrix is not diagonalizable, explain why. 9. Consider the...
LA class!!
1. Find a diagonlizing matrix P for the matrix A and write A in the form A = PDP-1 where D is a diagonal matrix. AE 5 -6 3 3 -4 3 0 0 2 Also, use the diagonalization of A to compute A8, A-8, and eA.
I
5.3: Diagonalization Find the diagonal matrix D and invertible matrix P such that A- PDp-1 if possible. If it is not possibl which eigenspace(s) are to blame. e, eosplain A-1 2 1 3 -1 A 1 1 1 5 0 3 A- 0 2 0 し406
5.3: Diagonalization Find the diagonal matrix D and invertible matrix P such that A- PDp-1 if possible. If it is not possibl which eigenspace(s) are to blame. e, eosplain A-1 2 1 3...
4. Consider the following matrix [1 0 -27 A=000 L-2 0 4] (a) (3 points) Find the characteristic polynomial of A. (b) (4 points) Find the eigenvalues of A. Give the algebraic multiplicity of each eigenvalue (c) (8 points) Find the eigenvectors corresponding to the eigenvalues found in part (b). (d) (4 points) Give a diagonal matrix D and an invertible matrix P such that A = PDP-1 (e) (6 points) Compute P-and verify that A= PDP- (show your steps).
Next Problem (1 point) Suppose 7 A 8 -5 Find an invertible matrix P and a diagonal matrix D so that A = PDP-1. Use your answer to find an expression for AⓇ in terms of P, a power of D, and P-1 in that order. -] 1/2 1 -1 0 -2 2 A6 1 1 0 3 2 -1 Note: In order to get credit for this problem all answers must be correct.
Name: 1. Find a diagonlizing matrix P for the matrix A and write A in the form A = PDP-1 where D is a diagonal matrix. 55 -6 37 A = 3 -4 31 To o 2 Also, use the diagonalization of A to compute AS, A-8, and e^. 2. Find the QR-decomposition of the following matrix: [ 1 2 2] A= 11 2 2 1 0 21 1-1 0 2] 3. Use the Gram-Schmidt process to construct an orthogonal...
Problem 8. a) Find the determinant det (A) for the matrix [1 -3 41 A 2 0 -1 1 b) Decide whether the matrix A has an inverse. If the inverse matrix A-1 exists, find its determinant det(A-1).
Diagonzalize the matrix A.
if possible. That is, find an invertible matrix P and 1 3 3 Diagonalize the matrix A= - 3 - 5 -3 3 3 a diagonal matrix D such that A = PDP-1. 1
Find a 3 × 3 matrix A with eigenvectors v1
= 1 2 3 with λ = 1, v2 = 0 −1 1 with λ = 2 and v3 =
1 1 1 with λ = 10. (Hint: A must be diagonalizable, A = P
DP −1 . Figure out P and D, then compute A directly.)
(6) Find a 3 x 3 matrix A with eigenvectors V1...
Find the eigenvalues of the given matrix. [-14 -6 36 16 1) A) -2.-4 B)-4 C)-2 D) -24 The characteristic polynomial of a 5 5 matrix is given below. Find the eigenvalues and their multiplicities 2) A5 - 24A4-189A3-486A2 2) A) 0 (multiplicity 2),-9 (multiplicity 2),-6 (multiplicity 1) B) 0 (multiplicity 1),9 (multiplicity 3), 6 (multiplicity ) C) 0 (multiplicity 2),9 (multiplicity 2),6 (multiplicity 1) D) 0 (multiplicity 2),-9 (multiplicity 2),6 (multiplicity 1) Diagonalize A- PDP-1 the matrix A, if...
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