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[M] In Exercises, find a factorization of the given matrix
Chapter 5, Problem 28E(choose chapter or problem)
[M] In Exercises 27 and 28, find a factorization of the given matrix A in the form \(A=P C P^{-1}\), where C is a block-diagonal matrix with \(2 \times 2\) blocks of the form shown in Example 6. (For each conjugate pair of eigenvalues, use the real and imaginary parts of one eigenvector in \(\mathbb{C}^{4}\) to create two columns of P.
\(\left[\begin{array}{rrrr}-1.4 & -2.0 & -2.0 & -2.0 \\ -1.3 & -.8 & -.1 & -.6 \\ .3 & -1.9 & -1.6 & -1.4 \\ 2.0 & 3.3 & 2.3 & 2.6\end{array}\right]\)
Questions & Answers
QUESTION:
[M] In Exercises 27 and 28, find a factorization of the given matrix A in the form \(A=P C P^{-1}\), where C is a block-diagonal matrix with \(2 \times 2\) blocks of the form shown in Example 6. (For each conjugate pair of eigenvalues, use the real and imaginary parts of one eigenvector in \(\mathbb{C}^{4}\) to create two columns of P.
\(\left[\begin{array}{rrrr}-1.4 & -2.0 & -2.0 & -2.0 \\ -1.3 & -.8 & -.1 & -.6 \\ .3 & -1.9 & -1.6 & -1.4 \\ 2.0 & 3.3 & 2.3 & 2.6\end{array}\right]\)
ANSWER:Solution 28E
Step 1
