The matrix

Algebra Level 5

\[ \left\{\begin{matrix} ax+by+cz=d\\ ex+fy+gz=h\\ jx+ky+lz=m \end{matrix}\right. \]

Let's say there is a system of three equations with variables \(x, y, z\) as above.

What is the minimum number of coefficients (denoted by letters \(a,b,c,e,f,g,j,k,l\)) that must be zero such that the system cannot be solved using Cramer's rule?

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