Question

Describe all solutions of Ax = 0 in parametric vector form, where A is row equivalent to the given matrix.

Answer 1

Given A is row equivalent to the matrix

Let A be the matrix of the system and row reduce the augmented matrix into echelon form

Applying

We see that,

Where is a basic variable and are free variables

Since

Let x = x₂u+x₃v+x₄w, where u = , v = and w =

This calculation shows that every solution is a linear combination of the vectors u, v and w. that is, the solution set is span. Since neither of u, v nor w is a scalar multiple of the other, the solution set is a plane thorough the origin.