(a) Find the eigenvalues, eigenvectors and eigenspaces forA =1 0 53 6 02 0 10
Question
(a) Find the eigenvalues, eigenvectors and eigenspaces for
[ A = \begin{bmatrix} 1 & 0 & 5 \ 3 & 6 & 0 \ 2 & 0 & 1 \end{bmatrix} \
Solution
Sure, let's find the eigenvalues, eigenvectors, and eigenspaces for the matrix A = [[1, 0, 5], [3, 6, 0], [2, 0, 1]].
Step 1: Find the eigenvalues The eigenvalues are the roots of the characteristic equation, which is given by det(A - λI) = 0, where I is the identity matrix and λ are the eigenvalues.
The matrix (A - λI) is:
[[1-λ, 0, 5], [3, 6-λ, 0], [2, 0, 1-λ]]
The determinant of this matrix is (1-λ)((6-λ)(1-λ)) -
Similar Questions
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