Column swap in an augmented matrix

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SUMMARY

Swapping columns in an augmented matrix does not alter the solution set, provided the 'b' column remains unchanged. This operation merely reorders the variables, similar to rearranging equations without changing their inherent relationships. For example, transforming the equations 2x + 3y = 1 and x - 2y = 2 into 3y + 2x = 1 and -2y + x = 2 illustrates this principle. The interpretation of results may vary, but the solutions remain consistent.

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Shaybay92
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This may seem like a very obvious question, but I thought it may be some sort of trick that my lecturer thought I may overlook... Well, when swapping columns of an augmented matrix, the solution set is unchanged (as long as you don't swap the 'b' column) is this correct? It is only swapping the way the matrix is set out (and would give you a different route to solve) but the solutions should not be altered in anyway.
 
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Yes, basically, that is true- although it may change how you interpret the results. It is essentially the same as changing the equations

2x+ 3y= 1, x- 2y= 2 to 3y+ 2x= 1, -2y+ x= 2.

The only thing that has changed is which column represents "x" and which represents "y".
 

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