Practice Midterm 33A Spring '15
What's the difference between Gauss-Jordan elimination and row reducing to echelon form? and for Question 6, do we just need to prove that the elements are linearly independent to be a basis?
carRobinson: May 4, 2015, 1:38 p.m.
I believe that Gauss-Jordan is the same thing as row reducing. Guass-Jordan is the process, rref is the product. And for 6, yes, you have to prove that all are linearly independent to be in R4.
abbyto1607: May 4, 2015, 5:24 p.m.
In order to be a basis, the set has to be linearly independent AND span all of the vector space. So, for 6, we need to prove that the given set also spans all of $P_{3}$ (or for part two, all of $R^{4}$.
leopham: May 5, 2015, 12:05 a.m.
Gauss-Jordan elimination is the method you use to row reduce. And the echelon form is when your matrix is in form of identity matrix or at least close to one. which means you only have one leading 1 at each row.
momokoishii: May 5, 2015, 9:05 p.m.
I also don't understand how reducing to echelon form has eight options. How does that work?