In Problems 1 through 23, find an eigenvector corresponding to each eigenvalue of the given matrix.
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In Problems 1 through 23, find an eigenvector corresponding to
each eigenvalue of the given matrix....
3 7. If A is a 3x3 matrix with eigenvector o corresponding to an 1-21 eigenvalue...
3 7. If A is a 3x3 matrix with eigenvector o corresponding to an 1-21 eigenvalue of 5 and 2 corresponding to an eigenvalue of 2, and v= 7 [10] 4 find Av. 6
Find (as a unit vector with negative first term) an eigenvector of the matrix corresponding to...
Find (as a unit vector with negative first term) an eigenvector
of the matrix
corresponding to the eigenvalue lambda = 2
2 – 30 – 6 Find (as a unit vector with negative first term) an eigenvector of the matrix 0 2 0 corresponding to the eigenvalue 1 = 2 0 - 6 4 -4 1/3 x Preview Answer: 6V154 77 V154 154 3V154 154
4. (a) (6 marks) Let A be a square matrix with eigenvector v, and corresponding eigenvalue...
4. (a) (6 marks) Let A be a square matrix with eigenvector v, and corresponding eigenvalue 1. Let c be a scalar. Show that A-ch has eigenvector v, and corresponding eigenvalue X-c. (b) (8 marks) Let A = (33) i. Find the eigenvalues of A. ii. For one of the eigenvalues you have found, calculate the corresponding eigenvector. iii. Make use of part (a) to determine an eigenvalue and a corresponding eigenvector 2 2 of 5 - 1
The matrix A= is diagonalisable with eigenvalues 1, -2 and -2. An eigenvector corresponding to the...
The matrix A= is diagonalisable with eigenvalues 1, -2 and -2.
An eigenvector corresponding to the eigenvalue 1 is . Find an
invertible matrix M such that M−1AM= ⎛⎝⎜⎜⎜1000-2000-2⎞⎠⎟⎟⎟. Enter
the Matrix M in the box below.
Question 8: Score 0/2 1 3 -3 4 6 -6 8 The matrix A = 1-6 6 | is diagonalisable with eigenvalues 1,-2 and-2. An eigenvector corresponding to the eigenvalue 1 is -2 2 1 0 0 0 0-2 Find an invertible matrix...
2. Use the spectral decomposition (in reverse) to find the matrix A such that (1,-1,1) is an eigenvector with eigenvalue 2, and (2, 3, 1) and (4,-1,5) are eigenvectors with eigenvalue-3. 2. Use...
2. Use the spectral decomposition (in reverse) to find the matrix A such that (1,-1,1) is an eigenvector with eigenvalue 2, and (2, 3, 1) and (4,-1,5) are eigenvectors with eigenvalue-3.
2. Use the spectral decomposition (in reverse) to find the matrix A such that (1,-1,1) is an eigenvector with eigenvalue 2, and (2, 3, 1) and (4,-1,5) are eigenvectors with eigenvalue-3.
(1 point) The matrix. has an eigenvalue 1 of multiplicity 2 with corresponding eigenvector ü. Find...
(1 point) The matrix. has an eigenvalue 1 of multiplicity 2 with corresponding eigenvector ü. Find 1 and i. i = has an eigenvector ū =
(1 point) Suppose that the matrix A has repeated eigenvalue with the following eigenvector and generalized...
(1 point) Suppose that the matrix A has repeated eigenvalue with the following eigenvector and generalized eigenvector: X= -4 with eigenvector v = and generalized eigenvector ū= [] (-1) Write the solution to the linear system r' = Ar in the following forms. A. In eigenvalue/eigenvector form: t t [CO] = C1 + C2 + I g(t). e . - 1 B. In fundamental matrix form: [CO] C. As two equations: (write "c1" and "c2" for 1 and 2) X(t)...
Q7. (a) Find a basis for the eigenspace of the following matrix corresponding to the eigenvalue...
Q7. (a) Find a basis for the eigenspace of the following matrix corresponding to the eigenvalue X= 2: 4 -16 2 1 6 2 -1 8 (b) Suppose that the vector r is an eigenvector of the matrix A corresponding to the eigenvalue 1. Let n be a positive integer. What is A" equal to?
Q7. (a) Find a basis for the eigenspace of the following matrix corresponding to the eigenvalue...
Q7. (a) Find a basis for the eigenspace of the following matrix corresponding to the eigenvalue X= 2: 4 -1 6 2 16 2 -1 8 (b) Suppose that the vector z is an eigenvector of the matrix A corresponding to the eigenvalue 4. Let n be a positive integer. What is A"r equal to?
Verify that ; is an eigenvalue of A and that x; is a corresponding eigenvector. A...
Verify that ; is an eigenvalue of A and that x; is a corresponding eigenvector. A = [3 0 ] LO-3 14 = 3, x1 = (1, 0) 12 = -3, X2 = (0, 1) AX1 = = 3 = 11X1 10 -3 1 0 **(4- = -1) --- --6-418- | | |--[:)--- Ax2 = = -3 = 12x2 -3
3 7. If A is a 3x3 matrix with eigenvector o corresponding to an 1-21 eigenvalue of 5 and 2 corresponding to an eigenvalue of 2, and v= 7 [10] 4 find Av. 6
Find (as a unit vector with negative first term) an eigenvector
of the matrix
corresponding to the eigenvalue lambda = 2
2 – 30 – 6 Find (as a unit vector with negative first term) an eigenvector of the matrix 0 2 0 corresponding to the eigenvalue 1 = 2 0 - 6 4 -4 1/3 x Preview Answer: 6V154 77 V154 154 3V154 154
4. (a) (6 marks) Let A be a square matrix with eigenvector v, and corresponding eigenvalue 1. Let c be a scalar. Show that A-ch has eigenvector v, and corresponding eigenvalue X-c. (b) (8 marks) Let A = (33) i. Find the eigenvalues of A. ii. For one of the eigenvalues you have found, calculate the corresponding eigenvector. iii. Make use of part (a) to determine an eigenvalue and a corresponding eigenvector 2 2 of 5 - 1
The matrix A= is diagonalisable with eigenvalues 1, -2 and -2.
An eigenvector corresponding to the eigenvalue 1 is . Find an
invertible matrix M such that M−1AM= ⎛⎝⎜⎜⎜1000-2000-2⎞⎠⎟⎟⎟. Enter
the Matrix M in the box below.
Question 8: Score 0/2 1 3 -3 4 6 -6 8 The matrix A = 1-6 6 | is diagonalisable with eigenvalues 1,-2 and-2. An eigenvector corresponding to the eigenvalue 1 is -2 2 1 0 0 0 0-2 Find an invertible matrix...
2. Use the spectral decomposition (in reverse) to find the matrix A such that (1,-1,1) is an eigenvector with eigenvalue 2, and (2, 3, 1) and (4,-1,5) are eigenvectors with eigenvalue-3.
2. Use the spectral decomposition (in reverse) to find the matrix A such that (1,-1,1) is an eigenvector with eigenvalue 2, and (2, 3, 1) and (4,-1,5) are eigenvectors with eigenvalue-3.
(1 point) The matrix. has an eigenvalue 1 of multiplicity 2 with corresponding eigenvector ü. Find 1 and i. i = has an eigenvector ū =
(1 point) Suppose that the matrix A has repeated eigenvalue with the following eigenvector and generalized eigenvector: X= -4 with eigenvector v = and generalized eigenvector ū= [] (-1) Write the solution to the linear system r' = Ar in the following forms. A. In eigenvalue/eigenvector form: t t [CO] = C1 + C2 + I g(t). e . - 1 B. In fundamental matrix form: [CO] C. As two equations: (write "c1" and "c2" for 1 and 2) X(t)...
Q7. (a) Find a basis for the eigenspace of the following matrix corresponding to the eigenvalue X= 2: 4 -16 2 1 6 2 -1 8 (b) Suppose that the vector r is an eigenvector of the matrix A corresponding to the eigenvalue 1. Let n be a positive integer. What is A" equal to?
Q7. (a) Find a basis for the eigenspace of the following matrix corresponding to the eigenvalue X= 2: 4 -1 6 2 16 2 -1 8 (b) Suppose that the vector z is an eigenvector of the matrix A corresponding to the eigenvalue 4. Let n be a positive integer. What is A"r equal to?
Verify that ; is an eigenvalue of A and that x; is a corresponding eigenvector. A = [3 0 ] LO-3 14 = 3, x1 = (1, 0) 12 = -3, X2 = (0, 1) AX1 = = 3 = 11X1 10 -3 1 0 **(4- = -1) --- --6-418- | | |--[:)--- Ax2 = = -3 = 12x2 -3
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