$$A$$ system of equations represented by $$AX=0$$ where $$X$$ is a column vector of unknown and $$A$$ is a square matrix containing coefficients has a non-trival solution when $$A$$ is.

The rank of the matrix$$\left[ {\matrix{ 1 & 1 \cr 0 & 0 \cr } } \right]\,\,is$$

Consider the following statements:
S1: The sum of two singular n x n matrices may be non-singular
S2: The sum of two n x n non-singular matrices may be singular

Which of the following statements is correct?

The determinant of the matrix $$$\left[ {\matrix{ 2 & 0 & 0 & 0 \cr 8 & 1 & 7 & 2 \cr 2 & 0 & 2 & 0 \cr 9 & 0 & 6 & 1 \cr } } \right]\,\,is$$$