Answer
See answer below
Work Step by Step
We are given:
$f_1(x)=2-5x$
$f_2(x)=3+7x$
$f_3(x)=4-x$
The augmented matrix of this system is:
$\begin{bmatrix}
2 & -5\\
3&7\\
4 & -1
\end{bmatrix} \approx \begin{bmatrix}
2 & -5\\
0 & -19\\
0 & -9
\end{bmatrix} \approx \begin{bmatrix}
2 & -5\\
0& -19\\
0 & 0
\end{bmatrix}$
We can see that just only $f_3$ is linearly independent, hence the polinominals:
$f_1(x)=2-5x$
$f_2(x)=3+7x$
can span $f_1(x)$
