7. Describe all solutions for $A x=0$ in parametric vector form, where $A$ is given below. \[ A=\left[\begin{array}{ccc} 3 & -9 & 6 \\ -1 & 3 & -2 \end{array}\right] \]

Step 1 ：The given matrix equation is \(Ax = 0\), where \(A\) is a 2x3 matrix. To find the solution in parametric vector form, we need to perform Gaussian elimination on the augmented matrix [A|0] to bring it to row-echelon form. Then, we can express the solution in terms of free variables.

Step 2 ：The matrix \(A\) is: \[A=\left[\begin{array}{ccc} 3 & -9 & 6 \\ -1 & 3 & -2 \end{array}\right]\]

Step 3 ：We can multiply the second row by 3 and add it to the first row to get: \[A=\left[\begin{array}{ccc} 0 & 0 & 0 \\ -1 & 3 & -2 \end{array}\right]\]

Step 4 ：Then we can multiply the second row by -1 to get: \[A=\left[\begin{array}{ccc} 0 & 0 & 0 \\ 1 & -3 & 2 \end{array}\right]\]

Step 5 ：This is the row-reduced echelon form of the matrix \(A\). The solution to the equation \(Ax = 0\) can be expressed in parametric vector form as: \(x = t[1, -3, 2]\) where \(t\) is a parameter.

Step 6 ：\(\boxed{The solution to the equation Ax = 0 in parametric vector form is x = t[1, -3, 2], where t is a parameter.}\)