Am I going correctly? Any suggestion to improve solution method? Consider the following system of equations:
$$
\left[\begin{array}{cccc}
1 & 2 & 3 & 4 \\
5 & 6 & 7 & 8 \\
a & 9 & b & 10 \\
6 & 8 & 10 & 13
\end{array}\right]\left[\begin{array}{c}
x_{1} \\
x_{2} \\
x_{3} \\
x_{4}  \\
\end{array}\right]=\left[\begin{array}{c}
0 \\
0 \\
0 \\
0
\end{array}\right]
$$
The locus of all $(a, b) \in \mathbb{R}^{2}$ such that this system has at least two dis-
tinct solutions for $\left(x_{1}, x_{2}, x_{3}, x_{4}\right)$ is
My Approach:
Here equation will be $$ax1+bx2+cx3+dx4=0$$
Here no polynomial degree of x
and also there are atleast 2 distinct point
and the line passes through these points
$So$, $this$ $should$ $be$ $a$ $straight$ $line$

Hint: the determinant of the matrix is easily calculated: $-4a-4b+72$.  Now there are more than one solution iff that determinant equals zero.
