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What is the norm of $u=(1,-2,-4,5,3)$?
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Suppose $u=(1,-2,-4,5,3)$. To find $\|u\|$, we can first find $\|u\|^{2}=u \cdot u$ by squaring each component of $u$ and adding, as follows:
$$\|u\|^{2}=1^{2}+(-2)^{2}+(-4)^{2}+5^{2}+3^{2}=1+4+16+25+9=55$$
Then $\|u\|=\sqrt{55}$
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