Parametric Vector Form

Parametric vector form is a way of expressing solutions (the solution set) to a linear system by choosing free variables as parameters and expressing the pivot (dependent) variables in terms of those parameters. In other words, if you know that x is twice y, but y can be whatever number because its a free variable, x = 2y for any y. This can be expressed by following the following steps:

• Write the system of linear equations as a matrix
• RREF the matrix until you reach RREF or find an inconsistent system
• Once you do, split the matrix back into equations and express the known variables by its unknowns
• rewrite the solution as a vector, first of the coordinates (the m number of columns of the matrix)
• Express those coordinates as the rewritten form
• Split it into however many vectors is needed by grouping unknown terms (usually s or t)