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Let A be an n x n matrix that is similar to an upper triangular matrix, and that has the distinct eigenvalues 1, 2, , dk with corresponding multiplicities m1, m2,... , mk (k< n, m + m2 + + m = n). Show that det(A=

Let A be an n x n matrix that is similar to an upper triangular matrix, and that has the distinct eigenvalues 1, 2, , dk with corresponding multiplicities m1, m2,... , mk (k< n, m + m2 + + m = n). Show that det(A=

Advanced Engineering Mathematics
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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Let A be an n × n matrix that is similar to an upper triangular matrix, and that has the distinct eigenvalues 1, 2,· , dk with corresponding multiplicities m1, m2, ... , m: (k< n, m, + m2 + · … · + mp = n). Show that det(A= X" CS Scanned with CamScanner
Transcribed Image Text:Let A be an n × n matrix that is similar to an upper triangular matrix, and that has the distinct eigenvalues 1, 2,· , dk with corresponding multiplicities m1, m2, ... , m: (k< n, m, + m2 + · … · + mp = n). Show that det(A= X" CS Scanned with CamScanner
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