Solution Sets of Linear Systems
- Determine if the system has a nontrivial solution. Try to use as few row operations as possible. solution
![eqn](one.png)
- Write the solution set of the given homogeneous system in
parametric vector form. solution
\begin{align*}
x_1+3x_2+x_3 &= 0 \\ -4x_1-9x_2+2x_3&=0\\
-3x_2-6x_3 & = 0
\end{align*}
- Describe all solutions of \(A\vec x = \vec 0\) in parametric vector form, where \(A\) is row equivalent to the given matrix. solution
\[
\left[\begin{array}{rrrrrr}
{1} & {-4} & {-2}&{0} & {3} & {5} \\
{0} & {0} & {1} & {0} & {0} & {-1}\\
{0} &{0} &{0} &{0} & {1} & {-4} \\
{0} & {0} & {0} & {0} & {0} & {0}
\end{array}\right]\]