characteristic-equation

Let $T(n)$ be the recurrence relation defined as follows: $T(0) = 1$ $T(1) = 2$, and $T(n) = 5T(n - 1) - 6T(n - 2)$ for $n \geq 2$ Which one of the following statements is TRUE?

The Lucas sequence $$L_n$$ is defined by the recurrence relation: $${L_n} = {L_{n - 1}} + {L_{n - 2}}$$, for $$n \ge 3$$, with $${L_1} = 1$$ and $${L_2} = 3$$. Which one of the opt...

The larger of the two eigenvalues of the matrix $$\left[ {\matrix{ 4 & 5 \cr 2 & 1 \cr } } \right]$$ is ______.

Let $$A$$ be the $$2 \times 2$$ matrix with elements $${a_{11}} = {a_{12}} = {a_{21}} = + 1$$ and $${a_{22}} = - 1$$. Then the eigen values of the matrix $${A^{19}}$$ are

What are the eigen values of the matrix $$P$$ given below? $$$P = \left( {\matrix{ a & 1 & 0 \cr 1 & a & 1 \cr 0 & 1 & a \cr } } \right)$$$

What are the eigen values of the following $$2x2$$ matrix? $$$\left[ {\matrix{ 2 & { - 1} \cr { - 4} & 5 \cr } } \right]$$$

If $$A = \left[ {\matrix{ 1 & 0 & 0 & 1 \cr 0 & { - 1} & 0 & { - 1} \cr 0 & 0 & i & i \cr 0 & 0 & 0 & { - i} \cr } } \right]$$ the matrix $${A^4},$$ calculated by the use of Cayley...