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arrow_back Why is \(|c| ||y|| = ||cy|| \) where \(y\) is a vector and \(c\) is a constant?

by Platinum
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Why is \(|c| ||y|| = ||cy|| \) where \(y\) is a vector and \(c\) is a constant?

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

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

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

\(=|c| ||y||\)
by Platinum
(104,456 points)

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