I'm trying to figure out how to get scalar multiples so that a set of 2x3 matrices is linearly dependent. That is so when they are all multiplied and added they result in the zero matrix. I know that if a set of vectors or matrices can't be written as a linear combination of the vectors or matrices in the set then it's linearly independent.

Here is the set of 2x3 matrices and I want to know HOW the book obtained the scalars.

(1 -3 2) (-3 7 4) (-2 3 11)
(-4 0 5), (6 -2-7),(-1-3 2)

Now with the scalars.

5*(1-3 2) + 3*(-3 7 4) -2*(-2 3 11) = (0 0 0)
...(-4 0 5)..... (6 -2-7).....(-1 -3 2)... (0 0 0)