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 Apr26 revised Are these two permutation matrices equivalent? deleted 71 characters in body Apr26 comment Are these two permutation matrices equivalent? Thanks. 8 more chars to go Apr26 asked Are these two permutation matrices equivalent? Apr26 comment Does one always use augmented matrices to solve systems of linear equations? Awesome, a confirmation. Thanks again. Apr26 revised Does one always use augmented matrices to solve systems of linear equations? added 188 characters in body Apr26 accepted Does one always use augmented matrices to solve systems of linear equations? Apr26 comment Does one always use augmented matrices to solve systems of linear equations? Thank you! So sorry for the obvious messy question. Apr26 comment Does one always use augmented matrices to solve systems of linear equations? Updated the question, sorry for all the ambiguity. Apr26 revised Does one always use augmented matrices to solve systems of linear equations? added 278 characters in body Apr26 comment Does one always use augmented matrices to solve systems of linear equations? @HenrySwanson, great, so if you're provided a $A$ and a $B$, you must augment $B$ as $[A|b]$ to properly solve the matrix right? This is just basic linear algebra, as we've just covered basic concepts, without any fancy mathwork. Apr26 comment Does one always use augmented matrices to solve systems of linear equations? So basically my question is, if you were forced to use matrices instead of easier equation subtraction/elimination (from grade school), must you augment the $3$ and $6$ (i.e. $[A|b]$ to properly solve the matrix? Otherwise you're kind of not performing EROs to each side, if you only solve $[A]$ right? My question may seen stupidly obvious, but I guess I'm confused... Apr26 revised Does one always use augmented matrices to solve systems of linear equations? added 177 characters in body Apr26 comment Does one always use augmented matrices to solve systems of linear equations? Oh, I guess I meant, specific to linear algebra homework/test problems where you're given $Ax = b$ and told to solve it using matrix elimination. Sorry! Apr26 comment Does one always use augmented matrices to solve systems of linear equations? I'm afraid I still don't understand. Can't you perform row operations on just $[A]$ instead of $[A|b]$? Apr26 comment Does one always use augmented matrices to solve systems of linear equations? Why not? Are you saying you could rearrange the equations as $x + 0y - 3 = 0$ and $-x + y - 6 = 0$? Apr26 asked Does one always use augmented matrices to solve systems of linear equations? Feb26 accepted What is the intuitive meaning of the basis of a vector space and the span? Feb25 asked What is the intuitive meaning of the basis of a vector space and the span? Jan25 revised Order of operations of multiple Matrix Elementary Row Operations deleted 704 characters in body Jan25 comment Order of operations of multiple Matrix Elementary Row Operations I was finally able to reproduce this correct solution. Thank you for all your help.