409059659
Eigenvalues & EigenvectorsName __________

Calculate the determinant.

#1. \(\begin{vmatrix} -4 & -9\\4 & -5\\\end{vmatrix}\)
#2. \(\begin{vmatrix} 1 & 8\\-1 & 1\\\end{vmatrix}\)
#3. \(\begin{vmatrix} -2 & -6 & -10\\9 & -3 & 4\\8 & 3 & 3\\\end{vmatrix}\)
#4. \(\begin{vmatrix} -2 & 7 & -3\\3 & 6 & -7\\-10 & 5 & 1\\\end{vmatrix}\)

Compute the trace of matrix \(A\).

#5. \(A=\begin{bmatrix} 3 & -9\\-5 & 15\\\end{bmatrix}\)
#6. \(A=\begin{bmatrix} 8 & -3 & -2\\1 & 2 & 7\\9 & -3 & 5\\\end{bmatrix}\)

Compute the eigenvalues of matrix \(A\).

#7. \(A=\begin{bmatrix} -2 & 0\\0 & -2\\\end{bmatrix}\)
#8. \(A=\begin{bmatrix} 3 & 1\\0 & 2\\\end{bmatrix}\)
#9. \(A=\begin{bmatrix} 1 & 4 & -2\\0 & -1 & 0\\-2 & -4 & 1\\\end{bmatrix}\)
#10. \(A=\begin{bmatrix} -3 & 0 & 0\\0 & -3 & 0\\0 & 0 & 2\\\end{bmatrix}\)

Choose a set of correct eigenvectors of matrix \(A\).

#11. \(A=\begin{bmatrix} -2 & 0\\0 & -3\\\end{bmatrix}\)
#12. \(A=\begin{bmatrix} 1 & 0\\0 & 0\\\end{bmatrix}\)

Choose a set of correct eigenvectors for the matrix \(A\).

#13. \(A=\begin{bmatrix} -3 & 0 & 0\\0 & 1 & 0\\0 & 0 & 0\\\end{bmatrix}\)
#14. \(A=\begin{bmatrix} 1 & 0 & 0\\0 & -2 & 0\\0 & 0 & 0\\\end{bmatrix}\)
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