hitmankratos Posted August 25, 2011 Share Posted August 25, 2011 Hey everyone, I'm taking a Linear Algebra course, and we just started talking about matrices. So we were introduced to the elementary row operations for matrices which say that we can do the following: 1. Interchange two rows. 2. Multiply a row with a nonzero number. 3. Add a row to another one multiplied by a number. Now I understood from the lecture in class how to use these and all, but I want to understand the logic behind number 2 and 3? Is there a mathematical proof that shows that by adding row R1 to row R2 we are not changing the system of equation? Same thing with number 2, how can we just multiply a row without changing the solution set? Thanks in advance, Link to comment Share on other sites More sharing options...
DrRocket Posted August 25, 2011 Share Posted August 25, 2011 Hey everyone, I'm taking a Linear Algebra course, and we just started talking about matrices. So we were introduced to the elementary row operations for matrices which say that we can do the following: 1. Interchange two rows. 2. Multiply a row with a nonzero number. 3. Add a row to another one multiplied by a number. Now I understood from the lecture in class how to use these and all, but I want to understand the logic behind number 2 and 3? Is there a mathematical proof that shows that by adding row R1 to row R2 we are not changing the system of equation? Same thing with number 2, how can we just multiply a row without changing the solution set? Thanks in advance, It should be obvious that those operations are invertible, with an inverse of a type contained in your list of allowable operations, and that any solution of the original set of equations is a solution after any of the named operations are performed. Link to comment Share on other sites More sharing options...
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