eigenvectors

Consider the matrix $\begin{bmatrix}1 & k \\ 2 & 1\end{bmatrix}$, where $k$ is a positive real number. Which of the following vectors is/are eigenvector(s) of this matrix?

Let the sets of eigenvalues and eigenvectors of a matrix B be {λk | 1 ≤ k ≤ n} and {vk | 1 ≤ k ≤ n}, respectively. For any invertible matrix P, the sets of eigenvalues and eigenvec...

The state equation of a second order system is $\dot{x}(t) = Ax(t)$, $x(0)$ is the initial condition. Suppose $\lambda_1$ and $\lambda_2$ are two distinct eigenvalues of A and $v_1...

Let the sets of eigenvalues and eigenvectors of a matrix B be $$\{ {\lambda _k}|1 \le k \le n\} $$ and $$\{ {v_k}|1 \le k \le n\} $$, respectively. For any invertible matrix P, the...

The state equation of a second order system is $$x(t) = Ax(t),\,\,\,\,x(0)$$ is the initial condition. Suppose $$\lambda_1$$ and $$\lambda_2$$ are two distinct eigenvalues of A and...

Let M be a real 4 $$ \times $$ 4 matrix. Consider the following statements : S1: M has 4 linearly independent eigenvectors. S2: M has 4 distinct eigenvalues. S3: M is non-singular...

Consider a linear system whose state space Representation is $$\mathop x\limits^ \bullet \left( t \right) = AX\left( t \right).$$ If the initial state vector of the system is $$x\l...

The eigen values and the correspondinng eigen vectors of a $$2 \times 2$$ matrix are given by Eigen value $${\lambda _1} = 8$$ $${\lambda _2} = 4$$ Eigen vector $${V_1} = \left[ {\...

For the matrix $$\left[ {\matrix{ 4 & 2 \cr 2 & 4 \cr } } \right].$$ The eigen value corresponding to the eigen vector $$\left[ {\matrix{ {101} \cr {101} \cr } } \right]$$ is

Given the matrix $$\left[ {\matrix{ { - 4} & 2 \cr 4 & 3 \cr } } \right],$$ the eigen vector is