2. A nilpotent matrix is a square matrix A € Mnxn (F) such that Ak = 0, for some integer k. -3 1 0 2 3 -1 (b) Prove that every nilpotent matrix is not invertible. (a) Show that the matrix B = 1 2 - is nilpotent.
2. A nilpotent matrix is a square matrix A € Mnxn (F) such that Ak = 0, for some integer k. -3 1 0 2 3 -1 (b) Prove that every nilpotent matrix is not invertible. (a) Show that the matrix B = 1 2 - is nilpotent.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:2. A nilpotent matrix is a square matrix A € Mnxn (F) such that
Ak = 0,
for some integer k.
-3 1
0 2
3
-1
(b) Prove that every nilpotent matrix is not invertible.
(a) Show that the matrix B
=
1
2
-
is nilpotent.
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