# arrow_back Why is $|c| ||y|| = ||cy||$ where $y$ is a vector and $c$ is a constant?

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Why is $|c| ||y|| = ||cy||$ where $y$ is a vector and $c$ is a constant?

$|| cy || =\sqrt{(c\cdot y_1)^2+(c\cdot y_2)^2+...+(c\cdot y_n)^2}$

$=\sqrt{c^2\cdot (y_1^2+y_2^2+...+(y_n)^2)}$

$=c\cdot \sqrt{y_1^2+y_2^2+...+(y_n)^2}$

$=|c| ||y||$
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