For each of the following homogeneous systems of linear equations, find the dimension of

Step 1 of 8

(a)

Consider the homogeneous system,

\( \begin{aligned}x_{1}+3 x_{2} & =0 \\2 x_{1}+6 x_{2} & =0\end{aligned} \)

The objective is to find the dimension and a basis for the solution set.

Note that, the given system has two variables (namely,  ). That is,

Write the system in matrix notation as shown.

 \( \underbrace{\left[\begin{array}{ll}1 & 3 \\2 & 6\end{array}\right]}_{1} \underbrace{\left[\begin{array}{l}x_{1} \\x_{2}\end{array}\right]}_{\mathbf{x}}=\underbrace{\left[\begin{array}{l}0 \\0\end{array}\right]}_{0} \)