Consider the following family of (n × n)-matrices with their off-diagonal, off-left, and last-column entries are zero.   a)Calculate the determinant of A2 and A3   B) Now determine (with proof) det An for any ¨ n ∈ N ∗ . Your formula is correct agree with a) and also with the trivial case n = 1?​​​​​​​

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Consider the following family of (n × n)-matrices with their off-diagonal, off-left, and last-column entries are zero.

 

a)Calculate the determinant of A2 and A3

 

B) Now determine (with proof) det An for any ¨ n ∈ N ∗ . Your formula is correct agree with a) and also with the trivial case n = 1?​​​​​​​

An
X
-1
ao
X
an-2
-1 A+an-1/
Transcribed Image Text:An X -1 ao X an-2 -1 A+an-1/
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