1 (a) Let A = 12 Without using the characteristic equation of A, show that is an eigenvector of A, and find the corresponding eigenvalue. (b) A matrix B has eigenvectors () and (), with corresponding eigenvalues 15 and 10 respectively. (i) Write down a diagonal matrix D and an invertible matrix P such that B = PDP-1, and calculate P-1. (ii) Hence show that 18125 -16250 -16250 42500

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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1
(a) Let A =
12
Without using the characteristic equation of A, show that
is
an eigenvector of A, and find the corresponding eigenvalue.
(b) A matrix B has eigenvectors
() and (), with corresponding
eigenvalues 15 and 10 respectively.
(i)
Write down a diagonal matrix D and an invertible matrix P
such that B = PDP-1, and calculate P-1.
(ii) Hence show that
18125 -16250
–16250
42500
Transcribed Image Text:1 (a) Let A = 12 Without using the characteristic equation of A, show that is an eigenvector of A, and find the corresponding eigenvalue. (b) A matrix B has eigenvectors () and (), with corresponding eigenvalues 15 and 10 respectively. (i) Write down a diagonal matrix D and an invertible matrix P such that B = PDP-1, and calculate P-1. (ii) Hence show that 18125 -16250 –16250 42500
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