Find unknown element in a matrix

1. Oct 18, 2011

RedXIII

1. The problem statement, all variables and given/known data
Find all values of a for which the columns of the matrix are linearly dependent.

$$\left( {\begin{array}{*{20}c} 2 & 0 & 8 \\ { - 4} & 7 & a \\ 1 & { - 3} & 4 \\ \end{array}} \right)$$

2. Relevant equations

3. The attempt at a solution
So I took of rref of the matrix and found

$$\left( {\begin{array}{*{20}c} 1 & 0 & 4 \\ { - 0} & 1 & 0 \\ 0 & { 0} & a+16 \\ \end{array}} \right)$$

So then I have
a+16=0
a = -16

So that gives me 1 value which makes the columns of the matrix linearly dependent, but how do I find the other ones, or even know if more exist?

Thanks

2. Oct 18, 2011

Dick

You've got it. There is just the one value, a=(-16). Otherwise the columns of the reduced matrix are linearly independent.

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