Let M in RR^(m xx n) be a matrix with rank(M)=r and let M=U Sum V^(TT) be its compact SVD decomposition. In other words -U in R_(m xx r) is semi-orthogonal i.e. U^(TT)U=I_r -Σ in RR_(r xx r) is diagonal with strictly positive entries -V in RR_(n xx r) is semi-orthogonal i.e. V^(TT)V=I_r What is the rank of UV^(TT)?

Describe all solutions of Ax=0 in parametric vector form, where A is row equivalent to the given matrix
$$\left[\begin{array}{cccc}1& 3& 0& -4\\ 2& 6& 0& -8\end{array}\right]$$

Find, correct to the nearest degree, the three angles of the triangle with the given vertices
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Whether f is a function from Z to R if 
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b) ${\displaystyle f\left(n\right)=\sqrt{n^2+1}}$. 
c) ${\displaystyle f\left(n\right)=\frac{1}{n^2-4}}$.

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The solution set of $\tan <!--\; \; -->\mathrm{\theta <!--\; \theta \; -->}=3\cot <!--\; \; -->\mathrm{\theta <!--\; \theta \; -->}$ is

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