?

Linear Algebra

Free Version

Upgrade subject to access all content

Moderate

Norm of a Sum of Vectors

LINALG-ZXVZDB

Which of the following equals $\lVert v+w\rVert$, for all $v,w\in\mathbb{R}^n$?

A

$\lVert v\rVert+\lVert w\rVert$

B

$\lVert v\rVert^2+\lVert w\rVert^2$

C

$\sqrt{v\cdot v+2v\cdot w+w\cdot w}$

D

$\sqrt{\lVert v\rVert^2+\lVert w\rVert^2-\lVert v-w\rVert^2}$