- #1
Rijad Hadzic
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Homework Statement
This is a linear algebra problem. Sorry I wasn't sure it to put this on precalc or here.
Consider two systems of linear equations having augmented matrices [A:B_1] and [A:B_2] where the matrix of coefficients of both systems is the same 3x3 matrix A.
Is it possible for [A:B_1] to have a unique solution and [A:B_2] to have many solutions?
Homework Equations
The Attempt at a Solution
I know that the answer is no due to my textbook's answer page, but I'm still a little confused as to why.
With the B_1 matrix, since it's a unique solution, I expect it to be in rref, by way of Gauss Jordan elimination, since this is the first chapter and that's the only method we know so far.
that means x1 = r x2 = s x3 = t for the first matrix since the solution is unique.
The second one has the same matrix of coefficients A. Since B_1 has a unique solution, and the matrix A didn't change, it would thus be impossible to have a set of solutions that involves parameters right?