Find all values of $x$ for which $\text{rank}(A) = 2$.

Question

$\{\{-1,1,0,7\},\{-2,2,x,-7´\},\{-1,3,2,0\}\}$

I have tried this and I am getting a rank of $3$ for all values. Ia there any value that actually gives a rank of $2$.

Answer 1

Yes it has full rank 3, because if you suppress the third column (so this is independent from any value taken by $x$), the resulting $3 \times 3$ matrix $M$ is such that $det(M)=-42 \neq 0$.