$$\sum\limits_{x = 1}^{99} {{1 \over {x\left( {x + 1} \right)}}} $$ = _____________.

Consider the following $$2 \times 2$$ matrix $$A$$ where two elements are unknown and are marked by $$a$$ and $$b.$$ The eigenvalues of this matrix ar $$-1$$ and $$7.$$ What are the values of $$a$$ and $$b$$?
$$A = \left( {\matrix{ 1 & 4 \cr b & a \cr } } \right)$$

The product of the non-zero eigenvalues of
the matrix $$\left[ {\matrix{ 1 & 0 & 0 & 0 & 1 \cr 0 & 1 & 1 & 1 & 0 \cr 0 & 1 & 1 & 1 & 0 \cr 0 & 1 & 1 & 1 & 0 \cr 1 & 0 & 0 & 0 & 1 \cr } } \right]$$ is ____ .

Consider the matrix as given below. $$$\left[ {\matrix{ 1 & 2 & 3 \cr 0 & 4 & 7 \cr 0 & 0 & 3 \cr } } \right]$$$

Which of the following options provides the Correct values of the Eigen values of the matrix?