Answer
See below
Work Step by Step
Given $v_1$ and $v_2$ are vectors in a vector space $V$, and $u_1, u_2, u_3$ are each linear combinations of them
Obtain: $u_1=a_{11}v_1+a_{12}v_2\\
u_2=a_{21}v_1+a_{22}v_2\\
u_3=a_{31}v_1+a_{32}v_2$
We form a matrix from these equations:
$A=\begin{bmatrix}
a_{11} & a_{12}\\
a_{21} &a_{22}\\
a_{31} & a_{32}
\end{bmatrix}=\begin{bmatrix}
a_{11} & a_{12}\\
0 & a_{21}a_{12}-a_{11}a_{22}\\
0 & 0
\end{bmatrix}$
Since the last row is equal to $0$, hence $v_3$ can be written as a linear combination of $u_1$ and $u_2$
