91Ó°ÊÓ

Compute the determinant of each matrix. Determine if the matrix is invertible without computing the inverse. $$ \left[\begin{array}{rr} 4 & -2 \\ -4 & 3 \end{array}\right] $$

Find the particular solution. \(x_{n+1}=-2 x_{n}+8 x_{n-1}-45 ; x_{0}=11, x_{1}=-5\)

Compute the determinant of each matrix. Determine if the matrix is invertible without computing the inverse. $$ \left[\begin{array}{rr} 9 & 2 \\ -5 & 3 \end{array}\right] $$

Find all the eigenvalues and the corresponding eigenvectors for the following matrices. $$ \left[\begin{array}{rrr} 10 & -4 & 15 \\ 8 & -2 & 15 \\ -4 & 2 & -5 \end{array}\right] $$

Find all the eigenvalues and the corresponding eigenvectors for the following matrices. $$ \left[\begin{array}{rrr} -3 & 0 & 0 \\ 9 & 6 & 30 \\ -1 & -1 & -5 \end{array}\right] $$

Find the particular solution. \(x_{n+1}=3 x_{n}+28 x_{n-1}-150 ; x_{0}=13, x_{1}=-49\)

Compute the determinant of each matrix. Determine if the matrix is invertible without computing the inverse. $$ \left[\begin{array}{rr} 7 & 2 \\ 8 & -9 \end{array}\right] $$

Solve using Gaussian elimination. $$ \begin{array}{rr} x+y+2 z= & 5 \\ x+y+z= & -10 \\ 2 x+3 y+4 z= & 2 \end{array} $$

Find the particular solution. \(x_{n+1}=9 x_{n}-18 x_{n-1}+20 ; x_{0}=7, x_{1}=26\)

Find all the eigenvalues and the corresponding eigenvectors for the following matrices. $$ \left[\begin{array}{rrr} -5 & 8 & 2 \\ -15 & 18 & 4 \\ 45 & -48 & -10 \end{array}\right] $$