Question

Write the solution set of the given homogeneous system in parametric vector form. 0 where the solution set is x

Answer 1

`x_(1) + 3x_(2) + x_(3) = 0\\`

X =
`\left[\begin{array}{ccc}x_(1)\\x_(2)\\x_(3)\end{array}\right]` =
`\left[\begin{array}{ccc}5x_(3)\\-2x_(3)\\x_(3)\end{array}\right]` =
`x_(3) \left[\begin{array}{ccc}5\\-2\\1\end{array}\right]`

Explanation:

Parametric vector form is the set of equation which form a line. The parametric equation is set and the vector matrix is formed based on the given equation. The solution set of x is found by equating the 0. It express a set of explicit independent variables.