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?