If $A=\left[a_{i j}\right], 1 \leq i, j \leq n$ with $n \geq 2$ and $a_{i j}=i+j$ is a matrix, then the rank of $A$ is

$$ \text { If } A=\left[\begin{array}{lll} 1 & 0 & 2 \\ 2 & 1 & 3 \\ 3 & 2 & 4 \end{array}\right] \text {, then } A^2-5 A+6 I= $$

Sum of the positive roots of the equation $$ \left|\begin{array}{ccc} x^2+2 x & x+2 & 1 \\ 2 x+1 & x-1 & 1 \\ x+2 & -1 & 1 \end{array}\right|=0 \text { is } $$

If the solution of the system of simultaneous linear equations $x+y-z=6,3 x+2 y-z=5$ and $2 x-y-2 z+3=0$ is $x=\alpha, y=\beta, z=y$, then $\alpha+\beta=$