Set and . Note that and . is the 4 dimensional vector space of R having basis .
(a) Show that real numbers and are both in space by expanding the powers and expressing them as a linear combination of the basis vectors.
(b) Show that the vectors are linearly dependent.
(a) , which can be written as:
(since and )
Is this right?
(b) This is the HARD part! I know that the vectors are linearly dependent if there are in reals, NOt all 0, such that
But I cant' figure out how to prove/represent this. Can anyone show me?
I can't see where to get the two equations from (and those equations probably wouldn't be linear)?So you need to determine if there exist , , and such that . That gives you two equations for , , and .
That gives you two equations