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.
My Attempt:
(a) , which can be written as:
(since
and
)
Now,
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?