Compute the trace of matrix \(A\).
#1. \(A=\begin{bmatrix} -4 & -16\\7 & 28\\\end{bmatrix}\)
#2. \(A=\begin{bmatrix} 3 & -12\\-1 & 4\\\end{bmatrix}\)
#3. \(A=\begin{bmatrix} -1 & 1 & -4\\-3 & 8 & -37\\-5 & -1 & 10\\\end{bmatrix}\)
#4. \(A=\begin{bmatrix} 10 & 7 & 54\\10 & 6 & 52\\-2 & -7 & -22\\\end{bmatrix}\)
Compute the eigenvalues of matrix \(A\).
#5. \(A=\begin{bmatrix} 7 & 8\\-4 & -5\\\end{bmatrix}\)
#6. \(A=\begin{bmatrix} \frac{14}{11} & -\frac{12}{11}\\-\frac{2}{11} & \frac{19}{11}\\\end{bmatrix}\)
#7. \(A=\begin{bmatrix} \frac{4}{3} & 0 & -\frac{2}{3}\\\frac{1}{6} & 1 & -\frac{1}{3}\\-\frac{1}{3} & 0 & \frac{5}{3}\\\end{bmatrix}\)
#8. \(A=\begin{bmatrix} -2 & 1 & -\frac{1}{2}\\\frac{3}{4} & -\frac{3}{4} & \frac{3}{8}\\-\frac{1}{2} & \frac{5}{2} & -\frac{5}{4}\\\end{bmatrix}\)
Choose a set of correct eigenvectors of matrix \(A\).
#9. \(A=\begin{bmatrix} 15 & -24\\9 & -15\\\end{bmatrix}\)
#10. \(A=\begin{bmatrix} \frac{3}{2} & \frac{3}{2}\\-\frac{1}{2} & -\frac{1}{2}\\\end{bmatrix}\)
Choose a set of correct eigenvectors for the matrix \(A\).
#11. \(A=\begin{bmatrix} \frac{5}{2} & -\frac{1}{2} & 0\\-\frac{1}{2} & \frac{5}{2} & 0\\\frac{1}{4} & -\frac{1}{4} & 2\\\end{bmatrix}\)
#12. \(A=\begin{bmatrix} \frac{10}{9} & -\frac{7}{9} & -\frac{1}{3}\\-\frac{8}{9} & \frac{11}{9} & -\frac{1}{3}\\\frac{4}{9} & -\frac{10}{9} & \frac{2}{3}\\\end{bmatrix}\)