There are the following possibilities:

- All columns are independent
- The first and the second are dependent, but independent of the third
- The first and the third are dependent, but independent of the second
- The second and the third are dependent, but independent of the first
- All of them are dependent

Or, if you prefer, you can do this with the rows.

Now for each case, you can write down an equation and solve it for

*a*. For example,let me do the third case (first and third are dependent, but independent of the second).

If the third column is a multiple

*n* of the first one, you must have

1 =

*n* *a*
-2 = 2

*n*
*a* =

*n* 1

From the second equation you see that there is just one possibility for

*n*. Then you get a solution for

*a* from one of the others. Finally, use the remaining equation to see if this value indeed satisfies all of them. Then plug this value into the 4

*a* in the second column, and check that it is indeed independent of the first (and/or third)