Problem 7
A matrix \(A\) and one of its eigenvalues are given. Find an eigenvector of A for the given eigenvalue. $$ \begin{array}{l} A=\left[\begin{array}{cc} 16 & 6 \\ -18 & -5 \end{array}\right] \\ \lambda=4 \end{array} $$
Problem 8
A matrix \(A\) and one of its eigenvalues are given. Find an eigenvector of A for the given eigenvalue. $$ \begin{array}{l} A=\left[\begin{array}{cc} -2 & 6 \\ -9 & 13 \end{array}\right] \\ \lambda=7 \end{array} $$
Problem 9
A matrix \(A\) and one of its eigenvalues are given. Find an eigenvector of A for the given eigenvalue. $$ \begin{aligned} A &=\left[\begin{array}{ccc} -16 & -28 & -19 \\ 42 & 69 & 46 \\ -42 & -72 & -49 \end{array}\right] \\ \lambda &=5 \end{aligned} $$
Problem 10
A matrix \(A\) and one of its eigenvalues are given. Find an eigenvector of A for the given eigenvalue. $$ \begin{aligned} A &=\left[\begin{array}{ccc} 7 & -5 & -10 \\ 6 & 2 & -6 \\ 2 & -5 & -5 \end{array}\right] \\ \lambda &=-3 \end{aligned} $$
Problem 11
A matrix \(A\) and one of its eigenvalues are given. Find an eigenvector of A for the given eigenvalue. $$ \begin{array}{l} A=\left[\begin{array}{ccc} 4 & 5 & -3 \\ -7 & -8 & 3 \\ 1 & -5 & 8 \end{array}\right] \\ \lambda=2 \end{array} $$
Problem 12
Find the eigenvalues of the given matrix. For each eigenvalue, give an eigenvector. $$\left[\begin{array}{ll}-1 & -4 \\ -3 & -2\end{array}\right]$$
Problem 13
Find the eigenvalues of the given matrix. For each eigenvalue, give an eigenvector. $$\left[\begin{array}{ll}-4 & 72 \\ -1 & 13\end{array}\right]$$
Problem 14
Find the eigenvalues of the given matrix. For each eigenvalue, give an eigenvector. $$\left[\begin{array}{cc}2 & -12 \\ 2 & -8\end{array}\right]$$
Problem 15
Find the eigenvalues of the given matrix. For each eigenvalue, give an eigenvector. $$\left[\begin{array}{ll}3 & 12 \\ 1 & -1\end{array}\right]$$
Problem 16
Find the eigenvalues of the given matrix. For each eigenvalue, give an eigenvector. $$\left[\begin{array}{cc}5 & 9 \\ -1 & -5\end{array}\right]$$
