now you can use the inequality and the cauchy-schwarz inequality and from there it's trivial.
I googled and found something that seemed more complex than my Beginner's Linear Algebra course so can someone list me the steps in simplified form in order to prove this so that I can learn it?
Any help would be greatly appreciated!
Thanks in advance!
A general way to derive the triangle from the Cauchy–Schwarz inequality is shown in Wikipedia. To apply this to simple linear algebra, define the inner product of two vectors and , denoted by , to be . Also, let . Then . It is easy to check that and .
The Cauchy–Schwarz inequality then says that , while the triangle inequality says that .