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Problem. Let A=1-1-2-2-2 0-2 1 1 -1 21 0 (a) Find a Jordan form J for A (b) Find the change of ba...
Problem. Let A=1-1-2-2-2 0-2 1 1 -1 2 1 0 (a) Find a Jordan form J for A. (b) Find the change of ...
Problem. Let A=1-1-2-2-2 0-2 1 1 -1 2 1 0 (a) Find a Jordan form J for A. (b) Find the change of basis matrix X such that X AX -J
Problem. Let A=1-1-2-2-2 0-2 1 1 -1 2 1 0 (a) Find a Jordan form J for A. (b) Find the change of basis matrix X such that X AX -J
2. Matrix B is defined as, -31 B=10-2 0 0-2 a. Find the Jordan form of matrix B b. Find exp (Jt), where J is the Jordan form of matrix B c. Find exp (Bt) 2. Matrix B is defined as, -31 B=10-2...
2. Matrix B is defined as, -31 B=10-2 0 0-2 a. Find the Jordan form of matrix B b. Find exp (Jt), where J is the Jordan form of matrix B c. Find exp (Bt)
2. Matrix B is defined as, -31 B=10-2 0 0-2 a. Find the Jordan form of matrix B b. Find exp (Jt), where J is the Jordan form of matrix B c. Find exp (Bt)
Exercise 30. Let A be a 5 x 5 matrix. Find the Jordan canonical form J...
Exercise 30. Let A be a 5 x 5 matrix. Find the Jordan canonical form J under each of the following assumptions (i) A has only eigenvalue namely 4 and dim N(A- 41) = 4. one (ii) dim N(A 21) = 5. (ii dim N(A -I) = 3 and dim N (A 31) 2. (iv) det(A I) = (1 - )2(2 - A)2 (3 - ) and dim N(A - I) dim N(A - 21) 1 (v) A5 0 and...
Linear Algebra Problem! Problem 4 (Jordan Canonical Form). Let A be a matrix in C6,6 whose...
Linear Algebra Problem!
Problem 4 (Jordan Canonical Form). Let A be a matrix in C6,6 whose Jordan Canonical form is given by ON OON JODODD JODOC JOOD 000000 E C6,6 ] O O O O O As we gradually give you more and more information about A below, fill in the blanks in J (and explain how you know the filled in values are correct). You may choose to order the Jordan blocks however you wish. Note: during the interview,...
1 1 1 0 -5 0 -77 0 2. 0 2 2. Let A be a...
1 1 1 0 -5 0 -77 0 2. 0 2 2. Let A be a 4 x 5 matrix whose reduced row echelon form is R 0 0 0 3 LO 0 0 0 0 For parts (b) and (c), write the solution in parametric vector form. (a) (2 points) Is the equation Ax b consistent for all b in R4? Why or why not? (b) (4 points) Solve the equation Ax = 0. 4 -3 -3 (c) (3...
Linear Algebra: Show that for each i = 1, ..., n there is a natural number p. j- 1v1, . . . , Vnf is a canonical Let be...
Linear Algebra: Show that for each i = 1, ..., n there is a
natural number p.
j- 1v1, . . . , Vnf is a canonical Let be a linear operator on V and Jordan basis, ie. ΤΊβ is a canonical Jordan form. Show that for each i-1, . . . ,n there is some p є N such that (T-ÀI)" (vi-0, where is the diagonal entry of the matrix [T]β on the ith column.
j- 1v1, . ....
3. Consider 2 00 0 0 3 12 A=1-4 3 3-2 -2 21 0 You are...
3. Consider 2 00 0 0 3 12 A=1-4 3 3-2 -2 21 0 You are given that the characteristic polynomial of A is XA (z) = (z 2). Find the Jordan form J of A and find a matrix P such that P-1AP J. (You do not need to find P-1.) (You may use an online RREF calculator, but remember you only have an ordinary calculator in the exams.)
11 0 -1 21 Let the reduced echelon form of matrix A = 1 - i...
11 0 -1 21 Let the reduced echelon form of matrix A = 1 - i 2 -3 0 0 0 0 LO 0 0 0 1 a) Find the determinant of A. b) Show that the columns of A are not independent. c) Find the dimension and the bases for the null space of A.
1 1 -21 2. Problem 2 Let A= -1 2 1 0 1 -1/ (a) (1...
1 1 -21 2. Problem 2 Let A= -1 2 1 0 1 -1/ (a) (1 point) Find the eigenvalues and eigenvectors of A. Solution: vastam 2 101 - 60: (b) (1 point) Find the eigenvectors of A. Solution: (c) (1 point) Find an invertible matrix P such that P-AP = D, where D is a diagonal matrix. Solution:
three small problem!!!!! Problem 7: (9 total points) Let A 11 0 -1 2 1 -1...
three small problem!!!!!
Problem 7: (9 total points) Let A 11 0 -1 2 1 -1 3 -1 0 = 1 | -2 1 4 -13 3 -1 -5 1 -6 a) Find a basis for ker A. b) Find a 5 x 5 matrix M with rank 2 such that AM = 0, where is the 4 x 5 zero matrix. is the 4 x 5 zero matrix. Prove c) Suppose that B is a 5 x 5 matrix...
Problem. Let A=1-1-2-2-2 0-2 1 1 -1 2 1 0 (a) Find a Jordan form J for A. (b) Find the change of basis matrix X such that X AX -J
Problem. Let A=1-1-2-2-2 0-2 1 1 -1 2 1 0 (a) Find a Jordan form J for A. (b) Find the change of basis matrix X such that X AX -J
2. Matrix B is defined as, -31 B=10-2 0 0-2 a. Find the Jordan form of matrix B b. Find exp (Jt), where J is the Jordan form of matrix B c. Find exp (Bt)
2. Matrix B is defined as, -31 B=10-2 0 0-2 a. Find the Jordan form of matrix B b. Find exp (Jt), where J is the Jordan form of matrix B c. Find exp (Bt)
Exercise 30. Let A be a 5 x 5 matrix. Find the Jordan canonical form J under each of the following assumptions (i) A has only eigenvalue namely 4 and dim N(A- 41) = 4. one (ii) dim N(A 21) = 5. (ii dim N(A -I) = 3 and dim N (A 31) 2. (iv) det(A I) = (1 - )2(2 - A)2 (3 - ) and dim N(A - I) dim N(A - 21) 1 (v) A5 0 and...
Linear Algebra Problem!
Problem 4 (Jordan Canonical Form). Let A be a matrix in C6,6 whose Jordan Canonical form is given by ON OON JODODD JODOC JOOD 000000 E C6,6 ] O O O O O As we gradually give you more and more information about A below, fill in the blanks in J (and explain how you know the filled in values are correct). You may choose to order the Jordan blocks however you wish. Note: during the interview,...
1 1 1 0 -5 0 -77 0 2. 0 2 2. Let A be a 4 x 5 matrix whose reduced row echelon form is R 0 0 0 3 LO 0 0 0 0 For parts (b) and (c), write the solution in parametric vector form. (a) (2 points) Is the equation Ax b consistent for all b in R4? Why or why not? (b) (4 points) Solve the equation Ax = 0. 4 -3 -3 (c) (3...
Linear Algebra: Show that for each i = 1, ..., n there is a
natural number p.
j- 1v1, . . . , Vnf is a canonical Let be a linear operator on V and Jordan basis, ie. ΤΊβ is a canonical Jordan form. Show that for each i-1, . . . ,n there is some p є N such that (T-ÀI)" (vi-0, where is the diagonal entry of the matrix [T]β on the ith column.
j- 1v1, . ....
3. Consider 2 00 0 0 3 12 A=1-4 3 3-2 -2 21 0 You are given that the characteristic polynomial of A is XA (z) = (z 2). Find the Jordan form J of A and find a matrix P such that P-1AP J. (You do not need to find P-1.) (You may use an online RREF calculator, but remember you only have an ordinary calculator in the exams.)
11 0 -1 21 Let the reduced echelon form of matrix A = 1 - i 2 -3 0 0 0 0 LO 0 0 0 1 a) Find the determinant of A. b) Show that the columns of A are not independent. c) Find the dimension and the bases for the null space of A.
1 1 -21 2. Problem 2 Let A= -1 2 1 0 1 -1/ (a) (1 point) Find the eigenvalues and eigenvectors of A. Solution: vastam 2 101 - 60: (b) (1 point) Find the eigenvectors of A. Solution: (c) (1 point) Find an invertible matrix P such that P-AP = D, where D is a diagonal matrix. Solution:
three small problem!!!!!
Problem 7: (9 total points) Let A 11 0 -1 2 1 -1 3 -1 0 = 1 | -2 1 4 -13 3 -1 -5 1 -6 a) Find a basis for ker A. b) Find a 5 x 5 matrix M with rank 2 such that AM = 0, where is the 4 x 5 zero matrix. is the 4 x 5 zero matrix. Prove c) Suppose that B is a 5 x 5 matrix...
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