Clearing fractions with row operations.

In summary, the conversation discusses the use of row operations in matrix manipulation and whether multiplying a row by a constant will always result in a unique row echelon form. The individual also mentions a software discrepancy and their own struggles with Gauss elimination. The final answer is that while upper triangular and row-echelon forms are not unique, reduced row-echelon forms are.
  • #1
skoker
10
0
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?
 
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  • #2
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.
 
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  • #3
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.
 

FAQ: Clearing fractions with row operations.

How do row operations help in clearing fractions?

Row operations can be used to manipulate the rows of a matrix in order to eliminate fractions and simplify the system of equations. This is done by multiplying a row by a non-zero constant or by adding or subtracting multiples of one row from another.

Can row operations be used on any type of matrix?

Yes, row operations can be used on any type of matrix, including square matrices, rectangular matrices, and augmented matrices. They are a fundamental tool in linear algebra and can be used to solve a variety of systems of equations.

What is the difference between a row operation and a column operation?

Row operations involve manipulating the rows of a matrix, while column operations involve manipulating the columns. Both types of operations can be used to simplify a system of equations, but they are not interchangeable and must be used correctly in order to maintain the accuracy of the system.

Can row operations change the solution to a system of equations?

No, row operations do not change the solution to a system of equations. They only manipulate the equations to make them easier to solve. As long as the operations are performed correctly, the solution to the system will remain the same.

Are there any limitations to using row operations?

There are some limitations to using row operations, such as not being able to divide by zero or not being able to add or subtract rows with different numbers of variables. It is important to carefully follow the rules of row operations in order to avoid any errors or inconsistencies in the solution.

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