H3 part b please Log InSep07SepRead your lecture notes and doH2. Let A5 be the matrix[22 -2A5 =51 -315-3(a) Use the eigenvalues of A5 to show that A5 is nilpotent.(b) Determine the smallest positive exponent k such that A5k = 0.H3. (a) Determine which of the matrices A1, ..., A4 from Questions 2.2.1 and H1 are nilpotent.(b) For each matrix in (a) that is nilpotent, determine the smallest positive exponent k suchthat Ajk = 0.Sec 2.3: 2, 3 (assume the notation in question 3 is referring to question 2).If any of the mathematics does not display properly (e.g., an error message received), comparewith this file.Recall that a scan of the instructor's lecture notes can be found in the Modules section of ourCanvas portal.Quiz 1 opens today; it is due Sept 18.Read your lecture notes and doq

Answered: ead your 12. Let A5 be the matrix [2 2…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Question

H3 part b please

Log In
Sep
07
Sep
Read your lecture notes and do
H2. Let A5 be the matrix
[22 -2
A5 =
51 -3
15-3
(a) Use the eigenvalues of A5 to show that A5 is nilpotent.
(b) Determine the smallest positive exponent k such that A5k = 0.
H3. (a) Determine which of the matrices A1, ..., A4 from Questions 2.2.1 and H1 are nilpotent.
(b) For each matrix in (a) that is nilpotent, determine the smallest positive exponent k such
that Ajk = 0.
Sec 2.3: 2, 3 (assume the notation in question 3 is referring to question 2).
If any of the mathematics does not display properly (e.g., an error message received), compare
with this file.
Recall that a scan of the instructor's lecture notes can be found in the Modules section of our
Canvas portal.
Quiz 1 opens today; it is due Sept 18.
Read your lecture notes and do
q

Expert Solution

Step 1

Here in the question, it is asked about the nilpotent matrix given in which the smallest positive exponent is to be find out such that ${A_{i}}^{k} = 0$ . A quadratic matrix If r is the smallest positive integer such that $A r = 0$ , then $A$ is referred to as a nilpotent matrix of degree $r$ . $A + B$ will be a nilpotent matrix if A and B are both nilpotent matrices.

We have to find the smallest positive exponent $k$ such that ${A_{i}}^{K} = 0$ . For this we have to see whether the matrix is nilpotent in which expoential term and equation.