Solution Sets of Linear Systems

  1. Determine if the system has a nontrivial solution. Try to use as few row operations as possible.  solution

    2. eqn

  2. Write the solution set of the given homogeneous system in parametric vector form.   solution

    3. \begin{align*} x_1+3x_2+x_3 &= 0 \\ -4x_1-9x_2+2x_3&=0\\ -3x_2-6x_3 & = 0 \end{align*}

  3. Describe all solutions of \(A\vec x = \vec 0\) in parametric vector form, where \(A\) is row equivalent to the given matrix.   solution

    4. \[ \left[\begin{array}{rrrrrr}
    {1} & {-4} & {-2}&{0} & {3} & {5} \\
    {0} & {0} & {1} & {0} & {0} & {-1}\\
    {0} &{0} &{0} &{0} & {1} & {-4} \\
    {0} & {0} & {0} & {0} & {0} & {0}
    \end{array}\right]\]