First off, I would like to apologize if this is the wrong forum I am posting in. I looked at all the forums and I believe that the Calculus forum is the most appropriate for this question, but if I made a wrong decision then I'm sorry!

The following equation system is a subspace in :

Questions:

How many dimensions is the subspace?

What is a basis for this subspace?

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Okay so first off, I want to figure out how many dimensions the subspace is.

I put the equation system into a totalmatrix:

I then find its parametric solution:

But here comes my problem...

According to my textbook, the answer is that it has 3 dimensions!

And in my parametric solution I only have 2 vectors (row 3 and 5) and two vectors only span over a 2 dimension!

So I have no idea what it is I have done wrong. Why am I not getting 3 dimensions like my textbook?