Problem 2 Consider the matrix A be given by 3. s 2 3 3 3 20 A = where s e R. a) Calculate the determinant of A(s) using a cofactor expansion, and determine for which s, A(s) is regular. Let s = 1 b) Determine the eigenvalues of A(1). c) Find the eigenvectors corresponding to each eigenvalue of A(1). d) Diagonalize A(1). That is, determine matrices P and D such that P'A(1)P = D.
Problem 2 Consider the matrix A be given by 3. s 2 3 3 3 20 A = where s e R. a) Calculate the determinant of A(s) using a cofactor expansion, and determine for which s, A(s) is regular. Let s = 1 b) Determine the eigenvalues of A(1). c) Find the eigenvectors corresponding to each eigenvalue of A(1). d) Diagonalize A(1). That is, determine matrices P and D such that P'A(1)P = D.
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Transcribed Image Text:Problem 2
Consider the matrix A be given by
2 s
3
s 2
3 3 20
A =
3
where se R.
a) Calculate the determinant of A(s) using a cofactor expansion, and determine for
which s, A(s) is regular.
Let s = 1
b) Determine the eigenvalues of A(1).
c) Find the eigenvectors corresponding to each eigenvalue of A(1).
d) Diagonalize A(1). That is, determine matrices P and D such that P-A(1)P = D.
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