Build matrix equations and uncover determinant solutions confidently. Inspect roots, tables, and visuals before answering. Built for practice, verification, reporting, and smarter problem solving.
Enter a 2×2 or 3×3 matrix. Each entry may be a constant or a linear expression in x, such as x, 2*x-3, -x+4, or 7.5.
| Matrix size | Determinant equation | Polynomial form | Real solutions |
|---|---|---|---|
| 3 × 3 | det([[x,2,1],[0,x-1,3],[1,4,2]]) = 10 | 2x^2 - 15x - 3 = 0 | x ≈ -0.195, 7.695 |
The calculator evaluates the determinant as a polynomial in x, then solves the equation det(A(x)) = target.
If A(x) = [[a, b], [c, d]], then det(A(x)) = ad - bc.
det(A(x)) = a(ei - fh) - b(di - fg) + c(dh - eg).
Because each entry is linear in x, the determinant becomes a polynomial of degree at most the matrix size. The script evaluates the determinant at several x values, interpolates the polynomial coefficients, subtracts the target, and solves the resulting equation.
It solves equations of the form det(A(x)) = target. The matrix can be 2×2 or 3×3, and each entry may be a constant or a linear expression in x.
You can enter values like x, -x, 2*x-3, 0.5*x+4, or plain constants. Nonlinear terms such as x², x/2, sin(x), or xy are intentionally rejected.
The determinant equation may produce complex solutions when the polynomial never crosses the target on the real axis. Complex roots still satisfy the algebraic equation.
The graph only shows real x values. If all solutions are complex, or real roots fall outside the selected graph range, no crossing marker appears.
Residual equals det(A(x)) minus the target after substituting a displayed real root. Values near zero confirm that the numerical solution is consistent.
No. This version focuses on 2×2 and 3×3 matrices so the determinant polynomial remains compact, fast to evaluate, and practical to solve accurately.
If the determinant polynomial becomes exactly equal to the target for all x, the script reports that every real x satisfies the equation.
Use exports when you need a quick report, want to save root values, or need a portable summary for homework, revision, or documentation.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.