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c. Find the change of coordinates matrix P from B to C.
[x]C = P [x]B

In short please make sure you copied the question correctly, as is it doesn't make sense.

In any case to check if a vector is in the span of that set, you can solve a system of equations.

You would use row reduction to verify if it is in the span.

To rephrase this you are seeing if x is in the image of A consisting of columns of B

Do this using row reduction. I will demonstrate.

alright, by the way abtrehearn thanks for the answer to part a it looks good

Now row reduce the matrix.

This would be the row reduced form?
1 0 0 1
0 1 0 1
0 0 1 -1
0 0 0 0

@ sir alchemista please solve my liinear algebra questions

But its not magic, you should understand the theory behind it.

Right on, DevinBlade :^)

Let me see...

Yep, there is already a solution in the new thread.