Jason
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 May 15 asked Basic independent probability question Apr 26 comment Does one always use augmented matrices to solve systems of linear equations? Wow, great additions, thanks. Apr 26 revised Are these two permutation matrices equivalent? deleted 71 characters in body Apr 26 comment Are these two permutation matrices equivalent? Thanks. 8 more chars to go Apr 26 asked Are these two permutation matrices equivalent? Apr 26 comment Does one always use augmented matrices to solve systems of linear equations? Awesome, a confirmation. Thanks again. Apr 26 revised Does one always use augmented matrices to solve systems of linear equations? added 188 characters in body Apr 26 accepted Does one always use augmented matrices to solve systems of linear equations? Apr 26 comment Does one always use augmented matrices to solve systems of linear equations? Thank you! So sorry for the obvious messy question. Apr 26 comment Does one always use augmented matrices to solve systems of linear equations? Updated the question, sorry for all the ambiguity. Apr 26 revised Does one always use augmented matrices to solve systems of linear equations? added 278 characters in body Apr 26 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. Apr 26 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... Apr 26 revised Does one always use augmented matrices to solve systems of linear equations? added 177 characters in body Apr 26 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! Apr 26 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 $[A|b]$? Apr 26 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 $-x + y - 6 = 0$? Apr 26 asked Does one always use augmented matrices to solve systems of linear equations? Feb 26 accepted What is the intuitive meaning of the basis of a vector space and the span? Feb 25 asked What is the intuitive meaning of the basis of a vector space and the span?