Chapter 13.4, Problem 30P

24.3. Show that 8 (a). =(+1)(z+1)*, |+1|<1, j=0 8 (b). sin³ z j=0 (-1) 3(1-9) 4 (2j+1)! 22j+1, |<∞,

24.4. For the function g(z) defined in (18.7), show that g(z) = j=0 z2j (−1)³ (2j+1)!" Hence, deduce that the function g(z) is entire. 2 E C.

h2

Use Laplace transform and convolution theorem to solve the initial value problem y' + y = tsint, y(0) = 0

Kindly inform what is bottling?

ם Hwk 25 Hwk 25 - (MA 244-03) (SP25) || X Answered: [) Hwk 25 Hwk 28 - (X + https://www.webassign.net/web/Student/Assignment-Responses/last?dep=36606604 3. [1.14/4 Points] DETAILS MY NOTES LARLINALG8 6.4.013. Let B = {(1, 3), (-2, -2)} and B' = {(−12, 0), (-4, 4)} be bases for R², and let 42 - [13] A = 30 be the matrix for T: R² R² relative to B. (a) Find the transition matrix P from B' to B. 6 4 P = 9 4 (b) Use the matrices P and A to find [v] B and [T(V)] B, where [v]B[31]. 26 [V] B = -> 65 234 [T(V)]B= -> 274 (c) Find P-1 and A' (the matrix for T relative to B'). -1/3 1/3 - p-1 = -> 3/4 -1/2 ↓ ↑ -1 -1.3 A' = 12 8 ↓ ↑ (d) Find [T(v)] B' two ways. 4.33 [T(v)]BP-1[T(v)]B = 52 4.33 [T(v)]B' A'[V]B' = 52 目 67% PREVIOUS ANSWERS ill ASK YOUR TEACHER PRACTICE ANOTHER

[) Hwk 25 Hwk 28 - (MA 244-03) (SP25) || X Success Confirmation of Questic X + https://www.webassign.net/web/Student/Assignment-Responses/submit?dep=36606607&tags=autosave#question 384855 DETAILS MY NOTES LARLINALG8 7.2.001. 1. [-/2.85 Points] Consider the following. -14 60 A = [ -4-5 P = -3 13 -1 -1 (a) Verify that A is diagonalizable by computing P-1AP. P-1AP = 具首 (b) Use the result of part (a) and the theorem below to find the eigenvalues of A. Similar Matrices Have the Same Eigenvalues If A and B are similar n x n matrices, then they have the same eigenvalues. (11, 12) = Need Help? Read It SUBMIT ANSWER 2. [-/2.85 Points] DETAILS MY NOTES LARLINALG8 7.2.007. For the matrix A, find (if possible) a nonsingular matrix P such that P-1AP is diagonal. (If not possible, enter IMPOSSIBLE.) P = A = 12 -3 -4 1 Verify that P-1AP is a diagonal matrix with the eigenvalues on the main diagonal. P-1AP = Need Help? Read It Watch It SUBMIT ANSWED 80% ill จ ASK YOUR TEACHER PRACTICE ANOTHER ASK YOUR…

[) Hwk 25 → C Hwk 27 - (MA 244-03) (SP25) IN X Answered: [) Hwk 25 4. [-/4 Poir X + https://www.webassign.net/web/Student/Assignment-Responses/submit?dep=36606606&tags=autosave#question3706544_6 3. [-/2.85 Points] DETAILS MY NOTES LARLINALG8 7.1.021. Find the characteristic equation and the eigenvalues (and a basis for each of the corresponding eigenspaces) of the matrix. 2 -2 5 0 3 -2 0-1 2 (a) the characteristic equation (b) the eigenvalues (Enter your answers from smallest to largest.) (1, 2, 13) = ·( ) a basis for each of the corresponding eigenspaces X1 x2 = x3 = Need Help? Read It Watch It SUBMIT ANSWER 4. [-/2.85 Points] DETAILS MY NOTES LARLINALG8 7.1.041. Find the eigenvalues of the triangular or diagonal matrix. (Enter your answers as a comma-separated list.) λ= 1 0 1 045 002 Need Help? Read It ASK YOUR TEACHER PRACTICE ANOTHER ASK YOUR TEACHER PRACTICE ANOTHER ill

[) Hwk 25 4. [-/4 Points] Hwk 25 - (MA 244-03) (SP25) || X Answered: Homework#7 | bartle X + https://www.webassign.net/web/Student/Assignment-Responses/last?dep=36606604 DETAILS MY NOTES LARLINALG8 6.4.019. Use the matrix P to determine if the matrices A and A' are similar. -1 -1 12 9 '-[ ¯ ¯ ], ^ - [ _—2—2 _ ' ], ^' - [ ˜³ −10] P = 1 2 A = -20-11 A' -3-10 6 4 P-1 = Are they similar? Yes, they are similar. No, they are not similar. Need Help? Read It SUBMIT ANSWER P-1AP = 5. [-/4 Points] DETAILS MY NOTES LARLINALG8 6.4.023. Suppose A is the matrix for T: R³ - → R³ relative to the standard basis. Find the diagonal matrix A' for T relative to the basis B'. A' = -1 -2 0 A = -1 0 0 ' 0 02 B' = {(−1, 1, 0), (2, 1, 0), (0, 0, 1)} ☐☐☐ ↓ ↑ Need Help? Read It Update available →] - restart now ASK YOUR T Sync and save data { Sign In ill ↑ New tab HT New window N New private window +HP ASK YOUR T Bookmarks History Downloads > > HJ Passwords Add-ons and themes HA Print... HP Save page as... HS…