# It's a bird! It's a plane! It's not superman...

Geometry Level 2

A system of three linear equations with three variables $$x, y, z$$ in the form

$\left\{\begin{matrix} ax+by+cz = d\\ ex+fy+gz = h \\ ix+jy+kz = l \end{matrix}\right.$

with $$(a, b, c, d, e, f, g, h, i, j, k, l) \in \mathbb{Z}$$ could be considered geometrically as three different planes intersecting each other in various ways, depending what those coefficients are. Some of the coefficients may be equal to other coefficients--or not.

Let $$\text{A}$$ be the coefficient matrix of that above system. If $$\text{det(A)} = 0$$, which of the following could be true about the system?

A. The planes are all parallel to each other.

B. A line is formed by the intersection of all three planes.

C. The planes form a triangular prism missing the triangular faces.

D. The planes all intersect at a single point.

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