True or False? If False, you should come up with a counterexample. If True, can you give a proof?
(a)
The zero vector is the only vector of length 0.
(b)
If , then .
(c)
If , then .
(d)
If , then .
(e)
If , then .
(f)
If for some scalar , then and have the same direction.
(g)
If , and are non-zero, and is parallel to , then and are also parallel.
(h)

Source

[Nicholson] W. Keith Nicholson, Linear Algebra with Applications, Lyryx 2021, Open Edition, Problem 4.1.21.

2024-09-06 02:05:50