If the system of equations, $x + 2y -3z = 1, (k + 3) z = 3, (2k + 1)x + z = 0$ is inconsistent, then the value of $k$ is :-

The roots of the determinant equation (in $x$) $\left| {\,\begin{array}{*{20}{c}}a&a&x\\m&m&m\\b&x&b\end{array}\,} \right| = 0$

In a third order determinant, each element of the first column consists of sum of two terms, each element of the second column consists of sum of three terms and each element of the third column consists of sum of four terms. Then it can be decomposed into $n $determinants, where $ n$  has the value

Statement $-1 :$Determinant of a skew-symmetric matrix of order $3$ is zero

Statement $-2 :$ For any matrix $A,$ $\det \left( {{A^T}} \right) = {\rm{det}}\left( A \right)$ and $\det \left( { – A} \right) = – {\rm{det}}\left( A \right)$ Where $\det \left( A \right) = A$. Then :

The values of $x,y,z$ in order of the system of equations $3x + y + 2z = 3,$ $2x – 3y – z = – 3$, $x + 2y + z = 4,$ are