Show that the given matrix is​ nilpotent, and then use this fact to find the matrix exponential eAt. A= −9 9 −1 −9 9 1 0 0 0

Q: Linear algebra. Please answer part (c)

A: Observe the general term as follows.

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A: We have to solve above matrix question

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A: Result: Let A be a diagonalizable matrix. Then, A=PDP-1 where columns of P are eigen vectors of A…

Q: Show that the given matrix is​ nilpotent, and then use this fact to find the matrix exponential eAt.…

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Q: Find an invertible matrix P and a diagonal matrix D such that P AP=D. 1 12 0-6 0 3 00 A = 0-36 1 18…

A: Given that, A=1120-603000-361180003We need to find an invertible matrix P and a diagonal matrix D…

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A: Any matrix , A is singular if, . Any matrix , A is non-singular if,   .

Q: 3. 7. Compute the matrix exponential eAt for the diagonal matrix A = 0 4 8. Use the formula et = L-'…

A: According to rule of bartleby I can solve only 1dt question if you need another kindly repost it For…

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A: Given : Matrix A = -8-1435   To find : Matrix Ak in the form of k?

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Q: 1. Find the inverse of the matrix. For what value(s) of x does the matrix have no a. [e* -e2x1 e 3x…

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Q: Let A be the given matrix. Find A-1 without a calculator. 00 1 A=100 010 A 1

A: The given matrix is A=001100010

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A: Answer  We will prove this by mathematical induction.

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A: Given A=10-4086001

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A: A matrix is said to be invertible if det A≠0 as A-1=1det(A)adjoint of A

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Q: Let A is an nxn matrix. Show that if A=A² , then (I-2A)=(I – 2A)

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Q: S)Give an example of a matrix A such that A2 = I but A#I or A± -I.

A: There are so many examples.

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Q: 3: Let A € Mnxn. Define the matrix exponential as e4 k! k=0 eA is always convergent and A° = I. a)…

A: (a).    Let the matrix A is diagonalizable.

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Q: Find an invertible matrix P and a diagonal matrix D such that PAP-D. -6-3 9 A = 5 2 -5 -3 -3 6 3x3…

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A: Solution:

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A: From the given problem: E=001010100 & A=-29-3325-4-97

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Q: 3. Let A be n x n matrix that has zeros on the main diagonal and ones everywhere else. Example of a…

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Q: Q3 Let A be n × n matrix that has zeros on the main diagonal and ones everywhere else. Example of a…

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Q: Let the charasteristic polynomial of a 3 x 3 matrix A be p(2) = 13- 1. Suppose that A2002 = aA? + bA…

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A: Definition used -                        If AX=B                       Then X= A-1B…

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A: Let A be 3 × 3 matrix such that  , A2 = A. Since we have given that , A = I3 and A = 0 are two…