Find a basis for the eigenspace corresponding to the eigenvalue of A given below. 4 0 - 1 A = 2 -8 , λ 3 1 - 2 - 2 A basis for the eigenspace corresponding to 2 = 3 is { }. (Use a comma to separate answers as needed.)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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**Finding a Basis for the Eigenspace Corresponding to the Eigenvalue**

Given Matrix A and Eigenvalue λ:

\[A = \begin{bmatrix}
4 & 0 & -1 \\
2 & 0 & -8 \\
1 & -2 & -2
\end{bmatrix}, \quad \lambda = 3\]

**Problem Statement:**
Find a basis for the eigenspace corresponding to the eigenvalue λ = 3.

**Solution:**
A basis for the eigenspace corresponding to λ = 3 is ⟨ [ ] ⟩. 
(Use a comma to separate answers as needed.)
Transcribed Image Text:**Finding a Basis for the Eigenspace Corresponding to the Eigenvalue** Given Matrix A and Eigenvalue λ: \[A = \begin{bmatrix} 4 & 0 & -1 \\ 2 & 0 & -8 \\ 1 & -2 & -2 \end{bmatrix}, \quad \lambda = 3\] **Problem Statement:** Find a basis for the eigenspace corresponding to the eigenvalue λ = 3. **Solution:** A basis for the eigenspace corresponding to λ = 3 is ⟨ [ ] ⟩. (Use a comma to separate answers as needed.)
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