Answer
$a=\dfrac{3}{2}$ and $b=\dfrac{1}{2}$
Work Step by Step
Let us consider that $u=2i+j,v=i+j,w=i-j$
Since, $u=av+bw$
and $2i+j=ai+aj+bi-bj$
Equate the terms. $a+b=2; a-b=1$
Solve the above two equations, we get $2a=3$
or, $a=\dfrac{3}{2}$
Now, $a+b=2$ or, $\dfrac{3}{2}+b=2$
and $b=\dfrac{1}{2}$
Hence, we have $a=\dfrac{3}{2}$ and $b=\dfrac{1}{2}$
