Find the values of x

Given the matrices

A=$\begin{pmatrix} 1-x & 1 & 0 \\ 1 & 1-x & 0 \\ -1 & x-1 & x \end{pmatrix} $  and B(x)= $\begin{pmatrix} 1 & 1 & x \\ -1 & x & 0 \\ -1 & x^{2} & x \end{pmatrix} $   ,   x ∈ R

a) Find the values of  x, at which   $det(A^{T}(x))≤det(−B(x))$ 

b) Find the values of  x, at which    rankA(x) ≤ rankB(x) = 2

Linear Algebra
Edintam372 Edintam372
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Aman R Aman R
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