Question
Asked Nov 1, 2019
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Problem 15.2. Let A be any complex n X n matrix. Prove that if A has the eigenvalue
0 with multiplicity n, then A" = 0. Give an example of a matrix A such that A" = 0 but
A 0
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Problem 15.2. Let A be any complex n X n matrix. Prove that if A has the eigenvalue 0 with multiplicity n, then A" = 0. Give an example of a matrix A such that A" = 0 but A 0

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Expert Answer

Step 1

Let 3x3 matrix A is given by,

0 1
A =0 0
0 0
0
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0 1 A =0 0 0 0 0

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Step 2

Let the Eigen value of the matrix A is λ.

The Eige...

0 0
1
A 0 0 0
0 0
0
Now, A-AI0
0-2
0 2
0
1
=0
0
0
0 A
0
0
-0+0(0+0+0) = 0
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0 0 1 A 0 0 0 0 0 0 Now, A-AI0 0-2 0 2 0 1 =0 0 0 0 A 0 0 -0+0(0+0+0) = 0

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