https://file.aiquickdraw.com/mathbot/file/17292363816712ni3zaoc.jpg

The image you've uploaded shows a 3x3 matrix with entries involving the variable \( \lambda \). This is likely part of an eigenvalue problem, where you're trying to solve for the eigenvalues by setting the determinant of the matrix equal to zero.

The matrix in the image is:

\[
\begin{pmatrix}
13 - \lambda & 5 & 2 \\
2 & 7 - \lambda & -8 \\
5 & 4 & 7 - \lambda
\end{pmatrix}
\]

To find the eigenvalues, we need to compute the determinant of this matrix and solve the characteristic equation \( \text{det}(A - \lambda I) = 0 \).

Let me calculate the determinant for you:

\[
\text{det}(A) = \begin{vmatrix} 13 - \lambda & 5 & 2 \\ 2 & 7 - \lambda & -8 \\ 5 & 4 & 7 - \lambda \end{vmatrix}
\]

Would you like me to go ahead and solve for the eigenvalues by expanding this determinant?

Solve for the eigenvalues of the following matrix: [[13 - λ, 5, 2], [2, 7 - λ, -8], [5, 4, 7 - λ]] by finding its determinant and solving det(A - λI) = 0.

Learn how to calculate the eigenvalues of a 3x3 matrix with variable λ by solving the determinant equation det(A - λI) = 0. This step-by-step solution covers key linear algebra concepts such as determinants and characteristic equations. Suitable for university-level linear algebra courses.

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