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Eigenvalues & EigenvectorsName __________

Compute the trace of matrix \(A\).

#1. \(A=\begin{bmatrix} 7 & -21\\-9 & 27\\\end{bmatrix}\)
#2. \(A=\begin{bmatrix} 9 & 18\\5 & 10\\\end{bmatrix}\)
#3. \(A=\begin{bmatrix} -4 & -8\\4 & -4\\\end{bmatrix}\)
#4. \(A=\begin{bmatrix} 2 & -6\\6 & -18\\\end{bmatrix}\)
#5. \(A=\begin{bmatrix} -10 & -10 & -40\\-7 & -6 & -23\\1 & -2 & -11\\\end{bmatrix}\)
#6. \(A=\begin{bmatrix} 6 & 1 & 0\\7 & 4 & 17\\3 & -2 & -15\\\end{bmatrix}\)

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

#7. \(A=\begin{bmatrix} 0 & -2\\0 & -2\\\end{bmatrix}\)
#8. \(A=\begin{bmatrix} -1 & 0\\0 & 0\\\end{bmatrix}\)
#9. \(A=\begin{bmatrix} 1 & 0\\3 & -2\\\end{bmatrix}\)
#10. \(A=\begin{bmatrix} 1 & 0\\0 & 1\\\end{bmatrix}\)
#11. \(A=\begin{bmatrix} -6 & -18\\3 & 9\\\end{bmatrix}\)
#12. \(A=\begin{bmatrix} -\frac{25}{11} & \frac{24}{11}\\\frac{12}{11} & \frac{3}{11}\\\end{bmatrix}\)

Compute the eigenvalues of matrix \(A\).

#13. \(A=\begin{bmatrix} \frac{29}{5} & -\frac{22}{5} & 10\\-\frac{22}{5} & -\frac{4}{5} & -5\\-4 & 2 & -7\\\end{bmatrix}\)
#14. \(A=\begin{bmatrix} -1 & -2 & 1\\0 & \frac{1}{3} & -\frac{1}{3}\\0 & -\frac{2}{3} & \frac{2}{3}\\\end{bmatrix}\)

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

#15. \(A=\begin{bmatrix} 1 & 0\\0 & 1\\\end{bmatrix}\)
#16. \(A=\begin{bmatrix} \frac{5}{2} & -\frac{1}{2}\\-\frac{3}{2} & \frac{3}{2}\\\end{bmatrix}\)
#17. \(A=\begin{bmatrix} 0 & 0\\0 & -1\\\end{bmatrix}\)
#18. \(A=\begin{bmatrix} -3 & 0\\6 & 0\\\end{bmatrix}\)
#19. \(A=\begin{bmatrix} 1 & 0\\0 & 3\\\end{bmatrix}\)
#20. \(A=\begin{bmatrix} 2 & 0\\1 & 3\\\end{bmatrix}\)
#21. \(A=\begin{bmatrix} -1 & \frac{9}{4}\\0 & 2\\\end{bmatrix}\)
#22. \(A=\begin{bmatrix} 1 & 2\\4 & -1\\\end{bmatrix}\)

Compute the trace of matrix \(A\).

#23. \(A=\begin{bmatrix} 1 & -8\\-5 & 6\\\end{bmatrix}\)
#24. \(A=\begin{bmatrix} -3 & 1\\8 & -10\\\end{bmatrix}\)
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