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Question 10 (10 points] Construct an example of a 2x2 matrix, with one of its eigenvalues...
Given the matrix 5 28 -16 A = 1 8 -4 E R3x3, 3 21 -11...
Given the matrix 5 28 -16 A = 1 8 -4 E R3x3, 3 21 -11 1. find all eigenvalues of A, 2. find the corresponding eigenvectors of A 3. show that A is diagonalizable, that is, find an invertible matrix KER3x3, and a diagonal matrix DE R3x3 such that 3. show that A is diagonalizable, that is, find an invertible matrix KER3x3, and a diagonal matrix DE R3x3 such that K-IAK = D.
step by step please Find the eigenvalues of the matrix and determine whether there is a...
step by step please
Find the eigenvalues of the matrix and determine whether there is a sufficient number to guarantee that the matrix is diagonalizable. (Recall that the matrix may be diagonalizable even though it is not guaranteed to be diagonalizable by the theorem shown below.) Sufficient Condition for Diagonalization If an n x matrix A has n distinct eigenvalues, then the corresponding cigenvectors are linearly independent and A is diagonalizable 02 Find the eigenvalues. (Enter your answers as a...
CengageBrain - My Home MA 313, section 202. OL, Summer 2 2020 [0.27/0.83 Points] DETAILS PREVIOUS...
CengageBrain - My Home MA 313, section 202. OL, Summer 2 2020 [0.27/0.83 Points] DETAILS PREVIOUS ANSWERS LARLINALG8 7.3.003. Prove that the symmetric matrix is diagonalizable. (Assume that a is real.) 00 a A= 0 a 0 а 0 0 Find the eigenvalues of A. (Enter your answers as a comma-separated list. Do not list the same eigenvalue multiple times.) X = 1,0,- 1 X Find an invertible matrix P such that p-1AP is diagonal. 0 -1 Ps 1 0...
Suppose that A is diagonalizable and all eigenvalues of A are positive real numbers. Prove that...
Suppose that A is diagonalizable and all eigenvalues of A are
positive real numbers. Prove that det (A) > 0.
(1 point) Suppose that A is diagonalizable and all eigenvalues of A are positive real numbers. Prove that det(A) > 0. Proof: , where the diagonal entries of the diagonal matrix D are Because A is diagonalizable, there is an invertible matrix P such that eigenvalues 11, 12,...,n of A. Since = det(A), and 11 > 0,..., n > 0,...
4.(5 pts)Give an example of a 3 x 3 matrix with eigenvalues of 2, 2, and...
4.(5 pts)Give an example of a 3 x 3 matrix with eigenvalues of 2, 2, and -3 that is diagonalizable. Show that it is, in fact, diagonalizable, and find C and D such that C (you may make this as trivial as you wish!) AC = D 5.(5 pts) Give an example of a 3 x 3 matrix with eigenvalues of 2, 2, and -3 that is NOT diagonalizable. Show WHY it is not diagonalizable. 6. (5 pts) Let T:...
please solve both 3. [-12 Points] DETAILS LARLINALG8 7.2.007. For the matrix A, find (if possible)...
please solve both
3. [-12 Points] DETAILS LARLINALG8 7.2.007. For the matrix A, find (if possible) a nonsingular matrix P such that p-1AP is diagonal. (If not possible, enter IMPOSSIBLE.) 8 -2 A= P= Verify that P-1AP is a diagonal matrix with the eigenvalues on the main diagonal. p-1AP = 1. [0/2 Points] DETAILS PREVIOUS ANSWERS LARLINALG8 7.2.001. Consider the following. -11 40 A= -27 (a) Verify that A is diagonalizable by computing p-1AP. -1 0 p-1AP = 10 3...
Question 12 [10 points] Find an invertible matrix P and a diagonal matrix D such that...
Question 12 [10 points] Find an invertible matrix P and a diagonal matrix D such that P-lAP=D. | 9 6 -2 A= -20 -13 4 | -24 -12 3 Tooo oool P= 0 0 0 D = 0 0 0 0 0 0 | 0 0 0 Official Time: 19:51:55 CS Scanned with CamScanner
Prove that if matrix A is diagonalizable with n real eigenvalues λι, λ2-..,An, then AI-λιλ2" λπ....
Prove that if matrix A is diagonalizable with n real eigenvalues λι, λ2-..,An, then AI-λιλ2" λπ. Complete the proof by justifying each step. There exists an invertible matrix P and a diagonal matrix D, such that P1AP -D. -JIAT O Determinant of a Matrix Product O Definition of the Inverse of a Matrix O Properties of the Identity Matrix O Determinant of a Triangular Matrix O Determinant of an Inverse Matrix O Definition of a Diagonalizable Matrix O Eigenvalues of...
[ 1 - 2. [20 points] Let A = 2. Construct a 2x2 matrix B (not...
[ 1 - 2. [20 points] Let A = 2. Construct a 2x2 matrix B (not the zero matrix) such that AB = 0. Show that the found matrix does work. 1-2 6
For the 3×2 matrix A: a) Determine the eigenvalues of ATA, and confirm that your eigenvalues...
For the 3×2 matrix A:
a) Determine the eigenvalues of ATA, and confirm that
your eigenvalues are consistent with the trace and determinant of
ATA.
b) Find an eigenvector for each eigenvalue of
ATA.
c) Find an invertible matrix P and a diagonal matrix D such that
P-1(ATA)P = D.
d) Find the singular value decomposition of the matrix A; that
is, find matrices U, Σ, and V such that A = UΣVT.
e) What is the best rank 1...
Given the matrix 5 28 -16 A = 1 8 -4 E R3x3, 3 21 -11 1. find all eigenvalues of A, 2. find the corresponding eigenvectors of A 3. show that A is diagonalizable, that is, find an invertible matrix KER3x3, and a diagonal matrix DE R3x3 such that 3. show that A is diagonalizable, that is, find an invertible matrix KER3x3, and a diagonal matrix DE R3x3 such that K-IAK = D.
step by step please
Find the eigenvalues of the matrix and determine whether there is a sufficient number to guarantee that the matrix is diagonalizable. (Recall that the matrix may be diagonalizable even though it is not guaranteed to be diagonalizable by the theorem shown below.) Sufficient Condition for Diagonalization If an n x matrix A has n distinct eigenvalues, then the corresponding cigenvectors are linearly independent and A is diagonalizable 02 Find the eigenvalues. (Enter your answers as a...
CengageBrain - My Home MA 313, section 202. OL, Summer 2 2020 [0.27/0.83 Points] DETAILS PREVIOUS ANSWERS LARLINALG8 7.3.003. Prove that the symmetric matrix is diagonalizable. (Assume that a is real.) 00 a A= 0 a 0 а 0 0 Find the eigenvalues of A. (Enter your answers as a comma-separated list. Do not list the same eigenvalue multiple times.) X = 1,0,- 1 X Find an invertible matrix P such that p-1AP is diagonal. 0 -1 Ps 1 0...
Suppose that A is diagonalizable and all eigenvalues of A are
positive real numbers. Prove that det (A) > 0.
(1 point) Suppose that A is diagonalizable and all eigenvalues of A are positive real numbers. Prove that det(A) > 0. Proof: , where the diagonal entries of the diagonal matrix D are Because A is diagonalizable, there is an invertible matrix P such that eigenvalues 11, 12,...,n of A. Since = det(A), and 11 > 0,..., n > 0,...
4.(5 pts)Give an example of a 3 x 3 matrix with eigenvalues of 2, 2, and -3 that is diagonalizable. Show that it is, in fact, diagonalizable, and find C and D such that C (you may make this as trivial as you wish!) AC = D 5.(5 pts) Give an example of a 3 x 3 matrix with eigenvalues of 2, 2, and -3 that is NOT diagonalizable. Show WHY it is not diagonalizable. 6. (5 pts) Let T:...
please solve both
3. [-12 Points] DETAILS LARLINALG8 7.2.007. For the matrix A, find (if possible) a nonsingular matrix P such that p-1AP is diagonal. (If not possible, enter IMPOSSIBLE.) 8 -2 A= P= Verify that P-1AP is a diagonal matrix with the eigenvalues on the main diagonal. p-1AP = 1. [0/2 Points] DETAILS PREVIOUS ANSWERS LARLINALG8 7.2.001. Consider the following. -11 40 A= -27 (a) Verify that A is diagonalizable by computing p-1AP. -1 0 p-1AP = 10 3...
Question 12 [10 points] Find an invertible matrix P and a diagonal matrix D such that P-lAP=D. | 9 6 -2 A= -20 -13 4 | -24 -12 3 Tooo oool P= 0 0 0 D = 0 0 0 0 0 0 | 0 0 0 Official Time: 19:51:55 CS Scanned with CamScanner
Prove that if matrix A is diagonalizable with n real eigenvalues λι, λ2-..,An, then AI-λιλ2" λπ. Complete the proof by justifying each step. There exists an invertible matrix P and a diagonal matrix D, such that P1AP -D. -JIAT O Determinant of a Matrix Product O Definition of the Inverse of a Matrix O Properties of the Identity Matrix O Determinant of a Triangular Matrix O Determinant of an Inverse Matrix O Definition of a Diagonalizable Matrix O Eigenvalues of...
[ 1 - 2. [20 points] Let A = 2. Construct a 2x2 matrix B (not the zero matrix) such that AB = 0. Show that the found matrix does work. 1-2 6
For the 3×2 matrix A:
a) Determine the eigenvalues of ATA, and confirm that
your eigenvalues are consistent with the trace and determinant of
ATA.
b) Find an eigenvector for each eigenvalue of
ATA.
c) Find an invertible matrix P and a diagonal matrix D such that
P-1(ATA)P = D.
d) Find the singular value decomposition of the matrix A; that
is, find matrices U, Σ, and V such that A = UΣVT.
e) What is the best rank 1...
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