## Thomas' Calculus 13th Edition

$a=\dfrac{3}{2}$ and $b=\dfrac{1}{2}$
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 $b=\dfrac{1}{2}$