2015年2月16日 · I'm sitting here doing rref problems and many of them seem so tedious. Any tricks out there to achieve rref with less effort or am I stuck with rewriting the matrix for every 2/3 operations? I know TI calculators can do it, but I'm gonna have to do this on my midterm, so I must learn how to do this the most efficient way possible. Thanks.

2016年3月29日 · $\begingroup$ Difference between REF and RREF: REF: 1.Each nonzero row lies above every zero row. 2. The leading entry of a nonzero row lies in a column to the right of the column with the leading entry of any preceding row.

All fine, yet I know that we have either a RREF (reduced row echelon form), where the leading entries are 1's and everything else in that same column is a 0 and REF where it's not essential that the other numbers are 0's and can be anything, as long as the pivots are 1's.

2016年1月24日 · $\begingroup$ Old thread, but in fact putting the vectors in as columns and then computing reduced row echelon form gives you more insight about linear dependence than if you put them in as rows.

2017年6月5日 · I have a quick question regarding the difference between echelon form and reduced row echelon form (rref). According to my googling these seem to be the same, but to me it seems that the difference between the two is that echelon form only requires the first value of the first row to be 1.

2015年5月23日 · When finding a basis for the row space of a matrix, I reduce the matrix to row echelon form, and find the rows that have pivots in them.

2019年8月21日 · Elementary row operations change the column space of the matrix, so you always have to go back to the original matrix to find a basis for its column space.

2015年8月4日 · When you look at the RREF of a square matrix augmented with the RHS, every complete row of zeros (last column included) corresponds to a free variable. A row of zeros also indicates infinitely many solutions. Therefore, it has to be "consistent" in this context.

2021年8月13日 · As for practical differences between REF and RREF, one practical difference is that in some situations it may be quicker or more computationally efficient to just compute REF. For example, solving a system of linear equations, it is typically quicker to just compute the REF of a system, and then solve the system by 'back substitution,' rather ...

2015年8月14日 · I've tried numerous other methods relying entirely on guess and check, but have not had any success. I want to know whether I am on the right track, and if so how I should continue to get to the final answer. I would also like to know whether or not there is a more systematic way of simplifying matrices into RREF form.