1042831072
Eigenvalues & EigenvectorsName __________

Calculate the determinant.

#1. \(\begin{vmatrix} 1 & -6\\-8 & 48\\\end{vmatrix}\)
#2. \(\begin{vmatrix} 8 & -32\\2 & -8\\\end{vmatrix}\)
#3. \(\begin{vmatrix} -2 & -6 & -24\\-3 & -8 & -34\\-8 & 4 & -40\\\end{vmatrix}\)
#4. \(\begin{vmatrix} 5 & 5 & 1\\7 & 10 & -2\\-4 & 1 & 2\\\end{vmatrix}\)

Compute the trace of matrix \(A\).

#5. \(A=\begin{bmatrix} 9 & -18\\6 & -12\\\end{bmatrix}\)
#6. \(A=\begin{bmatrix} -10 & 9 & 17\\-9 & 6 & 9\\-3 & 7 & 18\\\end{bmatrix}\)

Compute the eigenvalues of matrix \(A\).

#7. \(A=\begin{bmatrix} 3 & \frac{5}{4}\\0 & -2\\\end{bmatrix}\)
#8. \(A=\begin{bmatrix} \frac{5}{2} & -\frac{3}{8}\\-2 & \frac{3}{2}\\\end{bmatrix}\)
#9. \(A=\begin{bmatrix} -1 & 0 & 0\\-\frac{1}{2} & \frac{1}{2} & -\frac{1}{2}\\\frac{1}{2} & -\frac{3}{2} & -\frac{1}{2}\\\end{bmatrix}\)
#10. \(A=\begin{bmatrix} -3 & 3 & -6\\-5 & 7 & -10\\-\frac{5}{2} & \frac{7}{2} & -5\\\end{bmatrix}\)

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

#11. \(A=\begin{bmatrix} 2 & -\frac{8}{3}\\0 & -2\\\end{bmatrix}\)
#12. \(A=\begin{bmatrix} -3 & 0\\0 & -3\\\end{bmatrix}\)

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

#13. \(A=\begin{bmatrix} \frac{14}{3} & -\frac{8}{3} & 6\\\frac{14}{3} & -\frac{8}{3} & 6\\-\frac{2}{3} & \frac{2}{3} & -1\\\end{bmatrix}\)
#14. \(A=\begin{bmatrix} 4 & -4 & -2\\-1 & 1 & 2\\4 & -4 & -5\\\end{bmatrix}\)
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