Given the matrix $$A = \left[ {\matrix{ 0 & 1 & 0 \cr 0 & 0 & 1 \cr { - 6} & { - 11} & { - 6} \cr } } \right].\,\,$$ Its eigen values are

The rank of the following $$(n+1)$$ $$x$$ $$(n+1)$$ matrix, where $$'a'$$ is a real number is $$$\left[ {\matrix{ 1 & a & {{a^2}} & . & . & . & {{a^n}} \cr 1 & a & {{a^2}} & . & . & . & {{a^n}} \cr . & {} & {} & {} & {} & {} & {} \cr . & {} & {} & {} & {} & {} & {} \cr 1 & a & {{a^2}} & . & . & . & {{a^n}} \cr } } \right]$$$

The eigen values of the matrix $$\left[ {\matrix{ a & 1 \cr a & 1 \cr } } \right]$$ are

$$A$$ $$\,\,5 \times 7$$ matrix has all its entries equal to $$1.$$ Then the rank of a matrix is