Let $$\mathrm{S}$$ be the set of values of $$\lambda$$, for which the system of equations

$$6 \lambda x-3 y+3 z=4 \lambda^{2}$$,

$$2 x+6 \lambda y+4 z=1$$,

$$3 x+2 y+3 \lambda z=\lambda$$ has no solution. Then $$12 \sum_\limits{i \in S}|\lambda|$$ is equal to ___________.

Let A be a symmetric matrix such that $$\mathrm{|A|=2}$$ and $$\left[ {\matrix{ 2 & 1 \cr 3 & {{3 \over 2}} \cr } } \right]A = \left[ {\matrix{ 1 & 2 \cr \alpha & \beta \cr } } \right]$$. If the sum of the diagonal elements of A is $$s$$, then $$\frac{\beta s}{\alpha^2}$$ is equal to __________.

Let $$\mathrm{A_1,A_2,A_3}$$ be the three A.P. with the same common difference d and having their first terms as $$\mathrm{A,A+1,A+2}$$, respectively. Let a, b, c be the $$\mathrm{7^{th},9^{th},17^{th}}$$ terms of $$\mathrm{A_1,A_2,A_3}$$, respective such that $$\left| {\matrix{ a & 7 & 1 \cr {2b} & {17} & 1 \cr c & {17} & 1 \cr } } \right| + 70 = 0$$.

If $$a=29$$, then the sum of first 20 terms of an AP whose first term is $$c-a-b$$ and common difference is $$\frac{d}{12}$$, is equal to ___________.