3. Consider the following matrix: A = 122 21 2 2 11 212 (a) Determine the eigenvalues and the eigenvectors (b) Using Gram-Schmidt, construct an orthogonal basis set from the eigenvectors of this operation.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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3. Consider the following matrix:
[1
A = 2
2 21
1
L2 2
221
(a) Determine the eigenvalues and the eigenvectors
(b) Using Gram-Schmidt, construct an orthogonal basis set from the
eigenvectors of this operation.
4. Find the Fourier Transformer of the function:
f(x) = sin(wx), -1 < x < 1,
Fourier Transformer is defined by: F(u) =f(x)e-iux dx
1
where w is a constant
Transcribed Image Text:3. Consider the following matrix: [1 A = 2 2 21 1 L2 2 221 (a) Determine the eigenvalues and the eigenvectors (b) Using Gram-Schmidt, construct an orthogonal basis set from the eigenvectors of this operation. 4. Find the Fourier Transformer of the function: f(x) = sin(wx), -1 < x < 1, Fourier Transformer is defined by: F(u) =f(x)e-iux dx 1 where w is a constant
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