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Find the Basis of the System

Find the basis of the system $\alpha(2x-y-z) + \beta(y-z) – \gamma = 0$
So I find the matrix $[\alpha\beta\gamma]$ and plug in the numbers of my x and y.
The answer is $[1\ 0\ -1]$ which is not the same as $[1\ 0]$
so something is wrong.

A:

That is correct.
Consider another equation $x = x + 1$, which has the same set of solutions as $y = y – 1$.
Now, remove the first equation (which is the trivial equation $0 = 0$) and add another equation to the last (i.e. $z = z + 1$). You can check that the new system is equivalent to the original one. If you use the linear combination to calculate the basis in the $y$ and $z$ direction, you will get the same vector, but in the other order.
However, that doesn’t mean the two systems represent the same vector space. Your original system is closed under scalar multiplication, but the new system is not.

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How do you use the Sybase ODBC driver for Microsoft Access? I’m developing on Windows, but I’m connecting to a Sybase database via ODBC. The connection is successful, but I want to use Microsoft Access and my data files are in the Access format. I can read in my data files, but I can’t
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