Free 3x3 Cramer's rule calculator with a full determinant tableau. See D, Dx, Dy and Dz expanded along the first row, every replaced column highlighted, and the exact fraction solution with a back-substitution check.
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The Cramer's Rule Determinant Tableau turns a 2x2 or 3x3 linear system into the four determinants the method needs. Enter the coefficients in a labelled grid and see D plus one replacement determinant per variable, each expanded along the first row with its numeric minors, and the exact fraction ratios Dx/D, Dy/D and Dz/D.
Every value is computed with exact rational arithmetic, so fractions such as 14/11 stay exact. When D is zero the tableau still renders, and the system is classified by comparing the rank of the coefficient matrix with the rank of the augmented matrix rather than by the unreliable 'all determinants zero' shortcut.
Compute the coefficient determinant D, then replace the first, second and third column of the coefficient matrix with the constants to get Dx, Dy and Dz. When D is not zero, x = Dx/D, y = Dy/D and z = Dz/D.
Cramer's Rule does not apply, since dividing by zero is undefined. The system has either no solution or infinitely many, and the rank of the augmented matrix compared with the rank of the coefficient matrix decides which.
Not necessarily. The system x+y+z=1, x+y+z=2, x+y+z=3 has D, Dx, Dy and Dz all equal to zero but no solution at all, which is why the rank test is required.
Yes. Integers, decimals like 0.25 and fractions like 1/2 are all accepted and converted to exact rational numbers, so results never drift from rounding.
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