91Ó°ÊÓ

Using Jacobi's method, find the eigenvalues of the matrix \([A]\) given by $$ [A]=\left[\begin{array}{rrrr} 4 & -2 & 6 & 4 \\ -2 & 2 & -1 & 3 \\ 6 & -1 & 22 & 13 \\ 4 & 3 & 13 & 46 \end{array}\right] $$

Using the decomposition \([A]=[U]^{T}[U],\) find the inverse of the following matrix: $$ [A]=\left[\begin{array}{rrr} 5 & -1 & 1 \\ -1 & 6 & -4 \\ 1 & -4 & 3 \end{array}\right] $$

Using Choleski decomposition, find the inverse of the following matrix: $$ [A]=\left[\begin{array}{ccc} 2 & 5 & 8 \\ 5 & 16 & 28 \\ 8 & 28 & 54 \end{array}\right] $$

Using the Choleski decomposition technique, express the following matrix as the product of two triangular matrices: $$ [A]=\left[\begin{array}{rrr} 16 & -20 & -24 \\ -20 & 89 & -50 \\ -24 & -50 & 280 \end{array}\right] $$

Using MATLAB, find the eigenvalues and eigenvectors of the following matrix: $$ [A]=\left[\begin{array}{rrr} 3 & -2 & 0 \\ -2 & 5 & -3 \\ 0 & -1 & 1 \end{array}\right] $$

Using MATLAB, find the eigenvalues and eigenvectors of the following matrix: $$ [A]=\left[\begin{array}{rrr} -5 & 2 & 1 \\ 1 & -9 & -1 \\ 2 & -1 & 7 \end{array}\right] $$

Find the eigenvalues and eigenvectors of the following matrix using MATLAB: $$ [A]=\left[\begin{array}{rrr} 2 & 2 & 2 \\ 2 & 5 & 5 \\ 2 & 5 & 12 \end{array}\right] $$

Solve the following eigenvalue problem using MATLAB: $$ \omega^{2}\left[\begin{array}{lll} 3 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 1 \end{array}\right] \vec{X}=\left[\begin{array}{rrr} 10 & -4 & 0 \\ -4 & 6 & -2 \\ 0 & -2 & 2 \end{array}\right] \vec{X} $$