What does it mean when the determinant of the coefficient matrix comes out to be zero?
A zero determinant means the matrix is singular and has no inverse, so the neat X = A⁻¹B route fails.
A zero determinant means the matrix is singular and has no inverse, so the neat X = A⁻¹B route fails. Geometrically the equations are no longer independent: either they describe the same/parallel objects with no common point (no solution) or they overlap (infinitely many solutions). So det = 0 is your warning that the system does NOT have a single unique solution — you then check consistency to see which case it is.
Key point
det A = 0 ⇒ singular ⇒ the system has either no solution or infinitely many (never a unique one).
Common mistake
still expecting one unique answer when the determinant is zero.
Memory tip
det = 0 kills uniqueness — inspect for 'no solution' vs 'infinite solutions'.
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