?Inverse by Cayley-Hamilton For an invertible 3 ? 3 matrix A, we can write, using the
Chapter 5, Problem 67(choose chapter or problem)
Inverse by Cayley-Hamilton For an invertible 3 ⨉ 3 matrix A, we can write, using the Cayley-Hamilton Theorem, A3 + bA2 + cA + dI = 0, where b, c, and d are coefficients of the characteristic equation of A. If we multiply through on the left by A-1, we get A2 + bA + cI + dA-1 = 0, which can be solved for A-1. Use this method to calculate the inverses of Problems 67 and 68.
\(\left[\begin{array}{rrr} 2 & 0 & 0 \\ 1 & -1 & -3 \\ -1 & 0 & 1 \end{array}\right]\)
Equation Transcription:
Text Transcription:
[2 0 0 _ 1 -1 -3 _ -1 0 1]
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