I know the extended euclidean algorithm by working myself backward from the euclidean algorithm to find the GCD. I'm confused with the extended euclidean algorithm as given in this page. How is this process derived and why are we introducing new variables s and t? How is this process derived from working backwards with the standard euclidean algorithm? And how does the computation work now that we have $s_0, s_1, t_0, t_1$, which is neither intuitive nor any explanation is given anywhere.
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So if I have a matrix and I put it into RREF and keep track of the row operations, I can then write it as a product of elementary matrices. ...
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I am asked to prove the density of irrationals in $\mathbb{R}$. I understand how to do this by proving the density of $\mathbb{Q}$ first, na...
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Can someone just explain to me the basic process of what is going on here? I understand everything until we start adding 1's then after ...
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