Calculator
Enter matrix expressions using operators like +, -, *, /, and ^. Supported numeric functions include sqrt, abs, sin, cos, tan, log, ln, and exp.
Example Data Table
| Example | Matrix | Assignments | Symbolic Determinant | Numeric Result |
|---|---|---|---|---|
| Variable-rich 2 x 2 | [[x+1, 2], [y, x-3]] | x=5, y=4 | (x+1)(x-3) - 2y | 4 |
| Mixed 3 x 3 | [[x, 1, 2], [0, y, 3], [4, 5, 1]] | x=2, y=3 | x(y - 15) + 12 + 2(0 - 3*4) | -36 |
| Symbolic only | [[a, b], [c, d]] | None | ad - bc | Needs assignments |
Formula Used
For a 2 x 2 matrix
|a b; c d| = ad - bc
Each entry may itself contain variables or arithmetic expressions. Substitute known values first, then evaluate the determinant numerically.
For a 3 x 3 matrix
a(ei - fh) - b(di - fg) + c(dh - eg)
The calculator applies cofactor expansion along the first row after reading each symbolic matrix entry.
How to Use This Calculator
- Select either a 2 x 2 or 3 x 3 matrix.
- Type an expression into each visible matrix cell, such as x+1, 2*y, or sqrt(x).
- Enter numeric assignments in the format x=2, y=3 if you want a solved determinant value.
- Choose the decimal precision for the evaluated matrix and determinant.
- Press Calculate Determinant to show the result above the form.
- Download the output as CSV or PDF when a result is available.
FAQs
1. Can this calculator solve symbolic determinants without numbers?
Yes. It always builds the determinant expression symbolically. A final numeric answer appears only when every detected variable has an assigned numeric value.
2. Which matrix sizes are supported?
The page currently supports 2 x 2 and 3 x 3 matrices. Those sizes cover most educational and practical determinant exercises with variable entries.
3. What expression format should I use?
Use standard operators: +, -, *, /, and ^ for powers. Parentheses are supported. Write multiplication explicitly, so use 2*x instead of 2x.
4. Can I use trigonometric or root functions?
Yes. Supported functions include sqrt, abs, sin, cos, tan, log, ln, and exp. These functions work when enough numeric assignments are provided.
5. What happens if a variable is missing?
The calculator still shows the symbolic determinant. It also lists missing assignments, so you know exactly which variables must be defined for numeric evaluation.
6. How does the matrix type label work?
After numeric evaluation, a zero determinant marks the matrix as singular. Any nonzero determinant marks it as non-singular and therefore invertible.
7. What do the CSV and PDF downloads include?
They export the matrix size, variables, assignments, determinant expressions, final value, and status note. This makes reporting or classroom sharing much easier.
8. Is this calculator suitable for learning determinants?
Yes. It combines symbolic structure, substitution, evaluated matrices, formulas, examples, and short usage instructions, which makes it helpful for both practice and checking work.