CAPSTONE Consider the matrix below.A =[1010101010101010101010101](a) Is A symmetric?
Chapter 7, Problem 58(choose chapter or problem)
Consider the matrix below.
\(A=\left[\begin{array}{rrrrr}
-1 & 0 & -1 & 0 & 1 \\
0 & 1 & 0 & -1 & 0 \\
-1 & 0 & 1 & 0 & -1 \\
0 & -1 & 0 & -1 & 0 \\
1 & 0 & -1 & 0 & -1
\end{array}\right]\)
(a) Is A symmetric? Explain.
(b) Is A diagonalizable? Explain.
(c) Are the eigenvalues of A real? Explain.
(d) The eigenvalues of A are distinct. What are the dimensions of the corresponding eigenspaces? Explain.
(e) Is A orthogonal? Explain.
(f ) For the eigenvalues of A, are the corresponding eigenvectors orthogonal? Explain.
(g) Is A orthogonally diagonalizable? Explain.
Text Transcription:
A=[-1 0 -1 0 1
0 1 0 -1 0
-1 0 1 0 -1
0 -1 0 -1 0
1 0 -1 0 -1]
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