Chapter 1 Theorems

Theorems

1.12 If 2 matrices are row equivalent than the systems they represent (as augmented matrices) have:

the same solution set

1.18 Gauss-Jordan Elimination - Every matrix A is row equivalent to matrix B in:

row echelon form.

1.18 Gauss-Jordan Elimination - If B is in reduced row echelon form then B is:

unique (has one solution)

1.27 Rouché-Capelli - The system is inconsistent if and only if:

rref(A) has a pivot in the last column

1.27 Rouché-Capelli - The system has exactly one solution if and only if:

1. rref(A) does not have a pivot in the last column and

2. rref(C) has a pivot in every column

1.27 Rouché-Capelli - The system has infinitely many solutions if and only if:

1. rref(A) does not have a pivot in the last column and

2. rref(C) has a column without a pivot