The point P (a,b) undergoes the following three transformations successively :
(a) reflection about the line $\mathrm{y}=\mathrm{x}$.:
(b) translation through 2 units along the positive direction of $x$-axis.:
(c) rotation through angle $\frac{\pi}{4}$ about the origin in the anti-clockwise direction.:
If the co-ordinates of the final position of the point P are $\left(-\frac{1}{\sqrt{2}}, \frac{7}{\sqrt{2}}\right)$, then the value of $2 \mathrm{a}+\mathrm{b}$ is equal to: