Question

Describe all solutions of ax = 0 in parametric vector form, where a is row equivalent to the given matrix [ 3 -9 6 -1 3 -2 ]?

Answer 1

The solutions of the equation ax = 0 can be expressed in parametric vector form.

Step-by-step explanation:

To describe all solutions of the equation ax = 0 in parametric vector form, we need to find the values of x that satisfy the equation. Since a is row equivalent to the given matrix [ 3 -9 6 -1 3 -2 ], we can row reduce the matrix to find its row echelon form. Then, we can express the solutions in parametric form.

Row reducing the matrix [ 3 -9 6 -1 3 -2 ] gives us [ 1 -3 2 -1 0 -2 ]. Therefore, the general solution to the equation ax = 0 in parametric vector form is x = r(-3, -2, 1), where r is a scalar.