Give an example for each of the following, or explain why no example exists. (a) A...
For each of the following cases, provide an example satisfying the stated property, or state why it is impossible. (a) (b) A 2 x 2 matrix with singular values 1 and 2 so that ||A@1|| = 5. A 3 x 3 matrix with 3 real distinct eigenvalues so that 0 is an eigenvalue of A2 + 13.
9. For each of the following, provide a suitable example, or else explain why no such example exists. [2 marks each]. a) A function f : C+C that is differentiable only on the line y = x. b) A function f :C+C that is analytic only on the line y = x. c) A non-constant, bounded, analytic function f with domain A = {z | Re(z) > 0} (i.e., the right half-plane). d) A Möbius transformation mapping the real axis...
Give an example or explain why no such example exists: A regular eulerian graph with an even number of vertices and an odd number of edges.
Question 2. Give an example of the following, or if no example exists state that. As always, prove your answer in either casc. (a) A finite non-normal extension of Q (b) A finite non-normal extension of R (c) A finite non-normal extension of F7
2. A 5 x 5 matrix of real numbers, A s found to have the following eigenvalues (a) Explain why A is, or is NOT, diagonalizable. (b Explain why A is, or is NOT, inzertibie. 2. A 5 x 5 matrix of real numbers, A s found to have the following eigenvalues (a) Explain why A is, or is NOT, diagonalizable. (b Explain why A is, or is NOT, inzertibie.
Question 2. Give an example of the following, or if no example exists state that. As always, prove your answer in either case. (a) A finite non-normal extension of Q (b) A finite non-normal extension of R (c) A finite non-normal extension of F7 Question 2. Give an example of the following, or if no example exists state that. As always, prove your answer in either case. (a) A finite non-normal extension of Q (b) A finite non-normal extension of...
I need all details. Thx 2. Give an example of a matrix with the indicated properties. If the property cannot be attained, explain why not (a) A is 2 x 4 and has rank 3. (b) A is 3 × 3 and has determinant 1. (c) A is 3 × 6 and has a 3 dimensional row space and a 6 dinensional column space (d) A is 3 × 3 and has a 2 dimensional null space. (e) A is...
2. in problem 5.25 b) I can not solve this problem thank you Review Exercises 309 (c) Why is eA unitary? (d) Why is eKt unitary? 5.21 (a) Find a nonzero matrix N such that N3 0. (b) If Nx = Ax, show that λ must be zero. (c) Prove that N (called a "nilpotent" matrix) cannot be symmetric 5.22 Suppose the first row of A is 7, 6 and its eigenvalues are i, -i. Find A. 5.23 If the...
true or false and explain why (a) If the eigenvalues of a real symmetric matrix Anxn are all positive, then 7" A7 > 0 for any i in R" (b) If a real square matrix is orthogonally diagonalizable, it must be symmetric. (c) If A is a real mx n matrix, then both APA and AA' are semi-positive definite. (d) SVD and orthogonal diagonalization coincide when the real matrix concerned is symmetric pos- itive definite. (e) If vectors and q...
10. In each case, give an example (or explain why there isn't one) of a series a. ... that diverges, but (-1)"an converges. [1] b. ... that converges, but (-1)", diverges. [1] c. ... that diverges, but converges. [2] d. ... that converges, but a diverges. [2] e. ... that converges conditionally, but X(-1)"an converges absolutely. [2] that converges absolutely, but (-1)"an converges conditionally. [2] f.