eigenvectors

Suppose $\lambda$ is an eigenvalue of matrix A and $x$ is the corresponding eigenvector. Let $x$ also be an eigenvector of the matrix $\mathrm{B}=\mathrm{A}-2 \mathrm{I}$, where I...

For the matrix $[A] = \begin{bmatrix} 1 & -1 & 0 \\ -1 & 2 & -1 \\ 0 & -1 & 1 \end{bmatrix}$ which of the following statements is/are TRUE?

For the matrix [A] = [1 2 3] [3 2 1] [3 1 2] which of the following statements is/are TRUE?

For the matrix $[A]= \begin{bmatrix}1&2&3\\\ 3&2&1\\\ 3&1&2 \end{bmatrix} $ which of the following statements is/are TRUE?

For the matrix $\rm [A]=\begin{bmatrix}1&-1&0\\\ -1&2&-1\\\ 0&-1&1\end{bmatrix}$ which of the following statements is/are TRUE?

The matrix $\begin{pmatrix} 2 & -4 \ 4 & -2 \ \end{pmatrix}$ has

Consider the matrix $\begin{bmatrix} 5 & -1 \ 4 & 1 \end{bmatrix}$. Which one of the following statements is TRUE for the eigenvalues and eigenvectors of this matrix?

Consider the matrix $$\left[ {\matrix{ 5 & { - 1} \cr 4 & 1 \cr } } \right].$$ Which one of the following statements is TRUE for the eigenvalues and eigenvectors of this matrix?

Consider the system of equations, $${A_{nxn}}\,\,{X_{nx1}}\,\, = \lambda \,{X_{nx1}}$$ where $$\lambda $$ is a scalar. Let $$\left( {{\lambda _i},\,\,{X_i}} \right)$$ be an eigen v...

Obtain the eigen values and eigen vectors of $$A = \left[ {\matrix{ 8 & -4 \cr 2 & { 2 } \cr } } \right].$$