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Problem 31: Suppose A is a 2-by-2 real matrix for which 1 - 2i is an...
(1 point) Suppose A is a 3 x 3 matrix with real entries that has a...
(1 point) Suppose A is a 3 x 3 matrix with real entries that has a complex eigenvalue 2 - 5i with corresponding eigenvector 9+3i1 1 .Find another eigenvalue and 42 eigenvector for A. Eigenvalue Eigenvector-
(1 point) Suppose that the matrix A has the following eigenvalues and eigenvectors 2-2i and -2+2i Write the solution to...
(1 point) Suppose that the matrix A has the following eigenvalues and eigenvectors 2-2i and -2+2i Write the solution to the linear system AF in the following forms A. In eigenvalueleigenvector form r(t) B. In fundamental matrix form z(t) v(t) C. As two equations: (write "c1* and "c2" for ci and C2) a(t)- v(t)-
(1 point) Suppose that the matrix A has the following eigenvalues and eigenvectors 2-2i and -2+2i Write the solution to the linear system AF in the...
Suppose that the matrix A A has the following eigenvalues and eigenvectors: (1 point) Suppose that...
Suppose that the matrix A A has the following eigenvalues and
eigenvectors:
(1 point) Suppose that the matrix A has the following eigenvalues and eigenvectors: 2 = 2i with v1 = 2 - 5i and - 12 = -2i with v2 = (2+1) 2 + 5i Write the general real solution for the linear system r' = Ar, in the following forms: A. In eigenvalue/eigenvector form: 0 4 0 t MODE = C1 sin(2t) cos(2) 5 2 4 0 0...
Section 6.1 Eigenvalues and Eigenvectors: Problem 10 Previous Problem Problem List Next Problem 4 and the...
Section 6.1 Eigenvalues and Eigenvectors: Problem 10 Previous Problem Problem List Next Problem 4 and the determinant is det(A) --- 45. Find the eigenvalues of A. (1 point) Suppose that the trace of a 2 x 2 matrix A is tr(A) smaller eigenvalue larger eigenvalue Note: You can earn partial credit on this problem Preview My Answers Submit Answers Section 6.1 Eigenvalues and Eigenvectors: Problem 8 Previous Problem Problem List Next Problem (1 point) Find the eigenvalues di < 12...
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...
Problem #30: [2 marks] Suppose that a matrix A has characteristic polynomial p() = 1 -...
Problem #30: [2 marks] Suppose that a matrix A has characteristic polynomial p() = 1 - 31' + 814 - 23. Consider the following statements. (i) i = 2 is an eigenvalue of A. (ii) A is a 4 x 4 matrix. (iii) That same p() is also the characteristic polynomial of A! Determine which of the above statements are True (1) or False (2). So, for example, if you think that the answers, in the above order, are True...
<Problem 2> Answer the following questions about the square matrix A of order 3: A= III....
<Problem 2> Answer the following questions about the square matrix A of order 3: A= III. The square matrix B of order 3 is diagonalizable and meets AB=BA. prove that any eigenvector p of A is also an eigenvector of B. IV. Find the square matrix B of order 3 that meets B2 = A, where B is diagonalizable and all eigenvalues of B are positive. V. The square matrix X of order 3 is diagonalizable and meets AX =...
PROBLEM 3 (20%) Evaluate the following determinants: PROBLEM-i120%) Given the matrix 3 3 1 (a Fin...
help me solve problem 4,5 & 6
PROBLEM 3 (20%) Evaluate the following determinants: PROBLEM-i120%) Given the matrix 3 3 1 (a FindAby applying Gauss-Jordan elimination 3400 -3 2 5 2 -2I 1 500 0-2 3600-3 7 -700 1-2 (b) Find by applying determinant and matrix adjoint formula PROBLEM 5110961 Let Ade 2. evaluate 3a -3b -3c (b) ICId e f (c) IDIbeh (d)IE (e) 13A [ABC! IDEI PROBLEM 6 120%) Find a way to linearise the following equations, and...
LINEAR ALGEBRA What are the eigenvalues of the matrix 2-31 1 -2 1 What is the...
LINEAR ALGEBRA
What are the eigenvalues of the matrix 2-31 1 -2 1 What is the characteristic polynomial of this matrix? (That is, the polynomial you use to find the eigenvalues). 1-32 p() = -13 +212 -1. op() = X(4-1)(-2) op() = 12 + 1 OPW) = 12 -2X + 1. Let M = 2-31 1 -2 1 1-32 (this is the same as the previous problem). Find the eigenvalues of M (they are not listed according to multiplicity). Let...
Problem 2. (50 points) Suppose that a 4 x 4 matrix A with rows it. 73,...
Problem 2. (50 points) Suppose that a 4 x 4 matrix A with rows it. 73, 74, and has determinant det A = 1. Find the following determinants: ☺ U2 ü det 604 det det A +50 Note: You can earn partial creat on this problem Problem 1. (50 points) Let Rem -5 -20 -1 -1 - 1 4 16 0 الها (a) Compute dexA Use Cramer's rule to solve the following system 20x -5x -X -4 3 + 16x9...
(1 point) Suppose A is a 3 x 3 matrix with real entries that has a complex eigenvalue 2 - 5i with corresponding eigenvector 9+3i1 1 .Find another eigenvalue and 42 eigenvector for A. Eigenvalue Eigenvector-
(1 point) Suppose that the matrix A has the following eigenvalues and eigenvectors 2-2i and -2+2i Write the solution to the linear system AF in the following forms A. In eigenvalueleigenvector form r(t) B. In fundamental matrix form z(t) v(t) C. As two equations: (write "c1* and "c2" for ci and C2) a(t)- v(t)-
(1 point) Suppose that the matrix A has the following eigenvalues and eigenvectors 2-2i and -2+2i Write the solution to the linear system AF in the...
Suppose that the matrix A A has the following eigenvalues and
eigenvectors:
(1 point) Suppose that the matrix A has the following eigenvalues and eigenvectors: 2 = 2i with v1 = 2 - 5i and - 12 = -2i with v2 = (2+1) 2 + 5i Write the general real solution for the linear system r' = Ar, in the following forms: A. In eigenvalue/eigenvector form: 0 4 0 t MODE = C1 sin(2t) cos(2) 5 2 4 0 0...
Section 6.1 Eigenvalues and Eigenvectors: Problem 10 Previous Problem Problem List Next Problem 4 and the determinant is det(A) --- 45. Find the eigenvalues of A. (1 point) Suppose that the trace of a 2 x 2 matrix A is tr(A) smaller eigenvalue larger eigenvalue Note: You can earn partial credit on this problem Preview My Answers Submit Answers Section 6.1 Eigenvalues and Eigenvectors: Problem 8 Previous Problem Problem List Next Problem (1 point) Find the eigenvalues di < 12...
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...
Problem #30: [2 marks] Suppose that a matrix A has characteristic polynomial p() = 1 - 31' + 814 - 23. Consider the following statements. (i) i = 2 is an eigenvalue of A. (ii) A is a 4 x 4 matrix. (iii) That same p() is also the characteristic polynomial of A! Determine which of the above statements are True (1) or False (2). So, for example, if you think that the answers, in the above order, are True...
help me solve problem 4,5 & 6
PROBLEM 3 (20%) Evaluate the following determinants: PROBLEM-i120%) Given the matrix 3 3 1 (a FindAby applying Gauss-Jordan elimination 3400 -3 2 5 2 -2I 1 500 0-2 3600-3 7 -700 1-2 (b) Find by applying determinant and matrix adjoint formula PROBLEM 5110961 Let Ade 2. evaluate 3a -3b -3c (b) ICId e f (c) IDIbeh (d)IE (e) 13A [ABC! IDEI PROBLEM 6 120%) Find a way to linearise the following equations, and...
LINEAR ALGEBRA
What are the eigenvalues of the matrix 2-31 1 -2 1 What is the characteristic polynomial of this matrix? (That is, the polynomial you use to find the eigenvalues). 1-32 p() = -13 +212 -1. op() = X(4-1)(-2) op() = 12 + 1 OPW) = 12 -2X + 1. Let M = 2-31 1 -2 1 1-32 (this is the same as the previous problem). Find the eigenvalues of M (they are not listed according to multiplicity). Let...
Problem 2. (50 points) Suppose that a 4 x 4 matrix A with rows it. 73, 74, and has determinant det A = 1. Find the following determinants: ☺ U2 ü det 604 det det A +50 Note: You can earn partial creat on this problem Problem 1. (50 points) Let Rem -5 -20 -1 -1 - 1 4 16 0 الها (a) Compute dexA Use Cramer's rule to solve the following system 20x -5x -X -4 3 + 16x9...
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