Answer
$a=\dfrac{3}{2}$ and $b=\dfrac{1}{2}$
Work Step by Step
Suppose $u=2i+j,v=i+j,w=i-j$
The scalars $a,b$ can be found as: $u=av+bw$
Thus, $2i+j=ai+aj+bi-bj$
or, $a+b=2; a-b=1$
After solving the above two equations, we have $2a=3 \implies a=\dfrac{3}{2}$
From equation $a+b=2 \implies \dfrac{3}{2}+b=2$
or, $b=\dfrac{1}{2}$
Hence, $a=\dfrac{3}{2}$ and $b=\dfrac{1}{2}$
