466218986
Eigenvalues & EigenvectorsName __________

Calculate the determinant.

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

Compute the trace of matrix \(A\).

#5. \(A=\begin{bmatrix} -6 & 8\\9 & 4\\\end{bmatrix}\)
#6. \(A=\begin{bmatrix} -8 & 1 & -12\\6 & 10 & -34\\4 & -6 & 28\\\end{bmatrix}\)

Compute the eigenvalues of matrix \(A\).

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

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

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

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

#13. \(A=\begin{bmatrix} \frac{1}{2} & -\frac{1}{2} & -\frac{1}{4}\\-\frac{1}{2} & \frac{1}{2} & \frac{1}{4}\\0 & 0 & 0\\\end{bmatrix}\)
#14. \(A=\begin{bmatrix} 3 & 0 & 0\\6 & 3 & -3\\6 & 0 & 0\\\end{bmatrix}\)
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