MHB Clearing fractions with row operations.

[skoker]

i know you have the 3 row operations. add two rows. multiply a row by a constant. add a multiple of a row to another.

my question is can you multiply a row by a constant to clear a fraction at any time so long as you end up in row echelon form. no matter what operations you do the result in row echelon form will be unique?

i am checking my work with a software and when i do fraction free result it comes up with a different Gauss elimination then i do. but then when i put all the pivots to 1 for row echelon its the same result. is this going to give me problems in other thing? maybe where a Gauss elimination has to be unique?

 

[skoker]

Re: clearing fractions with row opperations.

so i think i figured it out. sorry if this is so basic, i just started in the linear algebra book.
i was doing the \( 3 \times 3, \; A^{-1} \) with Gauss elimination by hand and always getting it wrong.

 

[Deveno]

Re: clearing fractions with row opperations.

to answer your original question, the upper triangular and row-echelon forms of a matrix are not unique. the reduced row-echelon forms are, however.