Chapter 1 - Linear Equations in Linear Algebra - Supplementary Exercises - Page 91: 24

$b=-2 .a=\frac{-2 \sqrt{5}}{5}$

Solve equations: $2 a-4 b=2 \sqrt{5}$ $2 b+4 a=0$ Multiply second equation with 2 and add equations: $2 a-4 b+4 b+8 a=2 \sqrt{5}$ $10 a=2 \sqrt{5}$ $a=\frac{\sqrt{5}}{5}$ $2 b+4 a=0$ $2 b=-4 a$ $b=-2 a=\frac{-2 \sqrt{5}}{5}$