I need to express $(3,4,-2,-1)$ as a linear combination of $\frac{1}{2}(1,1,1,1) , \frac{1}{\sqrt{6}}(-1,-1,0,2)$ and $\frac{1}{\sqrt{50}}(-1,-3,6,-2)$
I create a system of linear equation:$$(3,4,-2,-1)=a\frac{1}{2}(1,1,1,1)+b\frac{1}{\sqrt{6}}(-1,-1,0,2)+c\frac{1}{\sqrt{50}}(-1,-3,6,-2)$$
The answer in my textbook is $a=2,b=-\frac{9}{\sqrt{6}},c=\frac{25}{\sqrt{50}}$
In any way I try to solve this system of equations, I fail to get these answers. Am I doing something wrong?