Exercise 8.1.5 Let 24 -4 -9 6 00 This matrix has eigenvalues λ = -3 and 2 = 4. Find a basis for each eigenspace. A =

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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Exercise 8.1.5**

Let 

\[ A = \begin{bmatrix} 2 & 4 & -4 \\ -1 & 6 & -9 \\ 0 & 0 & -3 \end{bmatrix} \]

This matrix has eigenvalues \( \lambda = -3 \) and \( \lambda = 4 \). Find a basis for each eigenspace.
Transcribed Image Text:**Exercise 8.1.5** Let \[ A = \begin{bmatrix} 2 & 4 & -4 \\ -1 & 6 & -9 \\ 0 & 0 & -3 \end{bmatrix} \] This matrix has eigenvalues \( \lambda = -3 \) and \( \lambda = 4 \). Find a basis for each eigenspace.
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Step 1: Determine the given matrix.

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