Prove that
$$2\sum_{k=1}^n\cos kθ= \frac{\sin\left(n+\frac12\right)θ}{\sin\fracθ2}-1$$
By using $$e^{iθ}+e^{2iθ}+\cdots+e^{niθ}=\frac{e^{iθ}(1-e^{inθ})}{1-e^{iθ}}$$
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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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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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