$\left| {\,\begin{array}{*{20}{c}}{bc}&{bc' + b'c}&{b'c'}\\{ca}&{ca' + c'a}&{c'a'}\\{ab}&{ab' + a'b}&{a'b'}\end{array}\,} \right|$ is equal to

Consider the system of linear equations

$x+y+z=5, x+2 y+\lambda^2 z=9$

$x+3 y+\lambda z=\mu$, where $\lambda, \mu \in R$. Then, which of the following statement is NOT correct?

If $a > 0$and discriminant of $a{x^2} + 2bx + c$is negative, then $\left| {\,\begin{array}{*{20}{c}}a&b&{ax + b}\\b&c&{bx + c}\\{ax + b}&{bx + c}&0\end{array}\,} \right|$ is

If $'a'$ is non real complex number for which system of equations $ax -a^2y + a^3z$ = $0$ , $-a^2x + a^3y + az$ = $0$ and $a^3x + ay -a^2z$ = $0$ has non trivial solutions, then $|a|$ is 

If ${A_i} = \left[ {\begin{array}{*{20}{c}}{{a^i}}&{{b^i}}\\{{b^i}}&{{a^i}}\end{array}} \right]$and if $|a|\, < 1,\,|b|\, < 1$, then $\sum\limits_{i = 1}^\infty {\det ({A_i})} $is equal to

The sum of distinct values of $\lambda$ for which the system of equations

$(\lambda-1) x+(3 \lambda+1) y+2 \lambda z=0$

$(\lambda-1) x+(4 \lambda-2) y+(\lambda+3) z=0$

$2 x+(3 \lambda+1) y+3(\lambda-1) z=0$

has non-zero solutions, is