The only way I can think of is to show they have the same characteristic polynomial; thus they have the same eigenvalues, But the question asked not to use determinants.
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The only way I can think of is to show they have the same
characteristic polynomial;...
A. The real eigenvalue(s) of the matrix is/areNe Type an Type each answer only once.) The...
A. The real eigenvalue(s) of the matrix is/areNe Type an Type each answer only once.) The matrix has no real eigenvalues. exact answer, using radicals as needed. Use a comma to separate answers as needed. O B. 2. Find the characteristic polynomial of the matrix, using either a cofactor expansion or the special formula for 3 x3 6 points)determinants. [Note: Finding the characteristic polynomial of a 3 x3 matrix is not easy to do with just row operation because the...
Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigenvalue for...
Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigenvalue for the matrix 1 A= = 66 -2) a) The characteristic polynomial is p(r) = det(A – r1) = b) List all the eigenvalues of A separated by semicolons. 1;-2 c) For each of the eigenvalues that you have found in (b) (in increasing order) give a basis of eigenvectors. If there is more than one vector in the basis for an eigenvalue, write them...
4. (Extra credit, all hand work. Use your paper and attach.) Let A-and assume a,b,ct are positivs. 0 b c (a) Let f) denote the characteristic polynomial of A. Calculate it and show work. You shou...
4. (Extra credit, all hand work. Use your paper and attach.) Let A-and assume a,b,ct are positivs. 0 b c (a) Let f) denote the characteristic polynomial of A. Calculate it and show work. You should get (b) Prove that A has only one real eigenvalue, that it is positive, and that the other two eigenvalues of A must be conjugate complex numbers. Let eigenvalues. λ denote the real positive eigenvalue and let λ2 and λ3 denote the other two...
Question 6 1 pts A 3x3 matrix with real entries can have (select ALL that apply)...
Question 6 1 pts A 3x3 matrix with real entries can have (select ALL that apply) (Hint: If you consider characteristic polynomial of the matrix then this is an algebra problem) one real eigenvalue and two complex eigenvalues. two real eigenvalues and one complex eigenvalue. three eigenvalues, all of them real. three eigenvalues, all of them complex. only two eigenvalues, both of them real. only one eigenvalue -- a complex one. only two eigenvalues, both of them complex only one...
Hello, I would like to discuss with someone the work that i've done on my own...
Hello,
I would like to discuss with someone the work that i've done
on my own regarding part d).
So we have d unique eigenvalues and d < n. if d=n, then we
only have a trivial solution (by the rank nullity theorem), but
this is a contradiction because v is a non-zero eigen vector.
hence the determinant (A- \lambda*I) =0. where this determinant
is equal to the characteristic polynomial equation.
The polynomial equation p(A)= \prod (A- \lambda_i * I)...
Suppose we have a quantum system with N eigenstates. Then we know the eigenstates can be...
Suppose we have a quantum system with N eigenstates. Then we know the eigenstates can be expressed as vectors, and operators can be represented by N × N matrices (a) Prove that (A)(A)where At is the transpose conjugate of matrix A. Here, A is not required to be Hermitian operator (Hint: express A and) in matrix and vector form. Use matrix calculation to show that (Αψ|U) is the same as 1Atlp.) (b) Prove that (ΑΒψ|U)-(ψ1BtAtlp). Á and B are not...
Let u and v be the vectors shown in the figure to the right, and suppose...
Let u and v be the vectors shown in the figure to the right, and suppose u and v are eigenvectors of a 2 x2 matrix A that correspond to eigenvalues -2 and 3, respectively. Let T: R2 R2 be the linear transformation given by T(x)-Ax for each x in R2, and let w-u+v. Plot the vectors T(u), T(v), and T(w). 2- u -2 2 4 -2 10- T(v) T(w -10 10 T(u) -10- Ay 10- T(v) T(w) T(u) 10...
Please show all work so I can gain a better understanding. Thank you! (Let X ⊂ R n be non-empty a...
Please show all work so I can gain a better understanding. Thank
you!
(Let X ⊂ R n be non-empty and let A be an n×n matrix. Show that
A[co (X)] = co (A[X]). Here co means convex hull.)
Exercise 17: Let X C Rn be non-empty and let A be an n × n matrix. Show that Alco (X)-co (A Here co means convex hull. )
Exercise 17: Let X C Rn be non-empty and let A be an...
Differention Equations - Can someone answer the checked numbers please? Determinants 659 is the characteristic equation of A with λ replaced by /L we can multiply by A-1 to get o get Now solve fo...
Differention Equations - Can someone answer the checked
numbers please?
Determinants 659 is the characteristic equation of A with λ replaced by /L we can multiply by A-1 to get o get Now solve for A1, noting that ao- det A0 The matrix A-0 22 has characteristic equation 0 0 2 2-A)P-8-12A +62- 0, so 8A1-12+6A -A, r 8A1-12 Hence we need only divide by 8 after computing 6A+. 23 1 4 12 10 4 -64 EXERCISES 1. Find AB,...
Book: A Course in Enumeration. Author: Martin Aigner Chapter 1 Page:29 According to this chapter, I think S n,k is the Stirling number and maybe the first kind. 1.37 Use the polynomial method to show...
Book: A Course in Enumeration. Author: Martin Aigner
Chapter 1 Page:29
According to this chapter, I think S n,k is the Stirling number
and maybe the first kind.
1.37 Use the polynomial method to show that sn lkti -o )sni Can you find a combinatorial proof?
1.37 Use the polynomial method to show that sn lkti -o )sni Can you find a combinatorial proof?
A. The real eigenvalue(s) of the matrix is/areNe Type an Type each answer only once.) The matrix has no real eigenvalues. exact answer, using radicals as needed. Use a comma to separate answers as needed. O B. 2. Find the characteristic polynomial of the matrix, using either a cofactor expansion or the special formula for 3 x3 6 points)determinants. [Note: Finding the characteristic polynomial of a 3 x3 matrix is not easy to do with just row operation because the...
Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigenvalue for the matrix 1 A= = 66 -2) a) The characteristic polynomial is p(r) = det(A – r1) = b) List all the eigenvalues of A separated by semicolons. 1;-2 c) For each of the eigenvalues that you have found in (b) (in increasing order) give a basis of eigenvectors. If there is more than one vector in the basis for an eigenvalue, write them...
4. (Extra credit, all hand work. Use your paper and attach.) Let A-and assume a,b,ct are positivs. 0 b c (a) Let f) denote the characteristic polynomial of A. Calculate it and show work. You should get (b) Prove that A has only one real eigenvalue, that it is positive, and that the other two eigenvalues of A must be conjugate complex numbers. Let eigenvalues. λ denote the real positive eigenvalue and let λ2 and λ3 denote the other two...
Question 6 1 pts A 3x3 matrix with real entries can have (select ALL that apply) (Hint: If you consider characteristic polynomial of the matrix then this is an algebra problem) one real eigenvalue and two complex eigenvalues. two real eigenvalues and one complex eigenvalue. three eigenvalues, all of them real. three eigenvalues, all of them complex. only two eigenvalues, both of them real. only one eigenvalue -- a complex one. only two eigenvalues, both of them complex only one...
Hello,
I would like to discuss with someone the work that i've done
on my own regarding part d).
So we have d unique eigenvalues and d < n. if d=n, then we
only have a trivial solution (by the rank nullity theorem), but
this is a contradiction because v is a non-zero eigen vector.
hence the determinant (A- \lambda*I) =0. where this determinant
is equal to the characteristic polynomial equation.
The polynomial equation p(A)= \prod (A- \lambda_i * I)...
Suppose we have a quantum system with N eigenstates. Then we know the eigenstates can be expressed as vectors, and operators can be represented by N × N matrices (a) Prove that (A)(A)where At is the transpose conjugate of matrix A. Here, A is not required to be Hermitian operator (Hint: express A and) in matrix and vector form. Use matrix calculation to show that (Αψ|U) is the same as 1Atlp.) (b) Prove that (ΑΒψ|U)-(ψ1BtAtlp). Á and B are not...
Let u and v be the vectors shown in the figure to the right, and suppose u and v are eigenvectors of a 2 x2 matrix A that correspond to eigenvalues -2 and 3, respectively. Let T: R2 R2 be the linear transformation given by T(x)-Ax for each x in R2, and let w-u+v. Plot the vectors T(u), T(v), and T(w). 2- u -2 2 4 -2 10- T(v) T(w -10 10 T(u) -10- Ay 10- T(v) T(w) T(u) 10...
Please show all work so I can gain a better understanding. Thank
you!
(Let X ⊂ R n be non-empty and let A be an n×n matrix. Show that
A[co (X)] = co (A[X]). Here co means convex hull.)
Exercise 17: Let X C Rn be non-empty and let A be an n × n matrix. Show that Alco (X)-co (A Here co means convex hull. )
Exercise 17: Let X C Rn be non-empty and let A be an...
Differention Equations - Can someone answer the checked
numbers please?
Determinants 659 is the characteristic equation of A with λ replaced by /L we can multiply by A-1 to get o get Now solve for A1, noting that ao- det A0 The matrix A-0 22 has characteristic equation 0 0 2 2-A)P-8-12A +62- 0, so 8A1-12+6A -A, r 8A1-12 Hence we need only divide by 8 after computing 6A+. 23 1 4 12 10 4 -64 EXERCISES 1. Find AB,...
Book: A Course in Enumeration. Author: Martin Aigner
Chapter 1 Page:29
According to this chapter, I think S n,k is the Stirling number
and maybe the first kind.
1.37 Use the polynomial method to show that sn lkti -o )sni Can you find a combinatorial proof?
1.37 Use the polynomial method to show that sn lkti -o )sni Can you find a combinatorial proof?
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