Compute the trace of matrix \(A\).
#1. \(A=\begin{bmatrix} 3 & -3\\-1 & 1\\\end{bmatrix}\)
#2. \(A=\begin{bmatrix} 2 & 9\\2 & 10\\\end{bmatrix}\)
#3. \(A=\begin{bmatrix} -10 & 6 & -10\\-5 & 3 & 8\\10 & 8 & 2\\\end{bmatrix}\)
#4. \(A=\begin{bmatrix} 4 & -5 & -42\\8 & 2 & -12\\-4 & -10 & -48\\\end{bmatrix}\)
Compute the eigenvalues of matrix \(A\).
#5. \(A=\begin{bmatrix} -3 & 0\\0 & -3\\\end{bmatrix}\)
#6. \(A=\begin{bmatrix} -\frac{3}{5} & -\frac{2}{5}\\-\frac{3}{5} & -\frac{2}{5}\\\end{bmatrix}\)
#7. \(A=\begin{bmatrix} 2 & 8 & 4\\-\frac{3}{2} & -5 & -2\\3 & 10 & 4\\\end{bmatrix}\)
#8. \(A=\begin{bmatrix} -\frac{1}{5} & 0 & \frac{8}{5}\\-\frac{6}{5} & 0 & -\frac{12}{5}\\\frac{8}{5} & 0 & \frac{11}{5}\\\end{bmatrix}\)
Choose a set of correct eigenvectors of matrix \(A\).
#9. \(A=\begin{bmatrix} 7 & 6\\-9 & -8\\\end{bmatrix}\)
#10. \(A=\begin{bmatrix} 1 & 0\\-6 & -1\\\end{bmatrix}\)
Choose a set of correct eigenvectors for the matrix \(A\).
#11. \(A=\begin{bmatrix} -\frac{5}{3} & -2 & \frac{2}{3}\\\frac{4}{3} & 3 & -\frac{4}{3}\\\frac{4}{3} & 4 & -\frac{7}{3}\\\end{bmatrix}\)
#12. \(A=\begin{bmatrix} 1 & 0 & 0\\0 & 0 & 0\\0 & 0 & 2\\\end{bmatrix}\)