Calculator
Example Data Table
| Example | Input A | Input B | Operation | Expected Result |
|---|---|---|---|---|
| Vector addition | (2, 3, 4) | (1, 0, -2) | Add | (3, 3, 2) |
| Dot product | (2, 3, 4) | (1, 0, -2) | Dot Product | -6 |
| Matrix multiplication | [[1, 2], [3, 4]] | [[5, 6], [7, 8]] | Multiply | [[19, 22], [43, 50]] |
| Determinant | [[1, 2], [3, 4]] | Not needed | Determinant | -2 |
| Inverse | [[4, 7], [2, 6]] | Not needed | Inverse | [[0.6, -0.7], [-0.2, 0.4]] |
Formula Used
Vector formulas
Vector addition uses component wise sums. Subtraction uses component wise differences. Dot product multiplies matching components and adds them. Cross product uses the three dimensional determinant pattern. Magnitude uses the square root of summed squares. Unit vector divides each component by the magnitude.
Angle uses cos(θ) = (A·B)/(‖A‖‖B‖). Distance uses ‖A − B‖. Projection of A on B uses ((A·B)/‖B‖²)B.
Matrix formulas
Matrix addition and subtraction combine matching entries. Matrix multiplication forms each result entry from a row and column dot product. Transpose swaps rows and columns. Determinant measures scaling for square matrices. Trace adds diagonal entries. Rank counts pivot rows after row reduction.
Inverse uses Gauss Jordan elimination on [A|I]. When the left side becomes I, the right side becomes A⁻¹.
How to Use This Calculator
- Choose Vector or Matrix from the calculation type list.
- Select the exact operation you want to run.
- Enter Vector A and Vector B with commas or spaces.
- Enter matrices using one row per line.
- Press Calculate to place the result below the header.
- Review the result table, steps, and graph.
- Use the export buttons to save CSV or PDF output.
Frequently Asked Questions
1. What vector operations are included?
The calculator handles addition, subtraction, dot product, cross product, magnitude, unit vector, angle, distance, and projection. Each operation shows working steps after submission.
2. What matrix operations are available?
You can add, subtract, multiply, transpose, find determinants, compute inverses, calculate trace, and estimate rank. Square matrix rules are checked automatically when required.
3. How should I type matrix values?
Enter one matrix row per line. Separate entries with commas or spaces. Every row must contain the same number of values for the matrix to parse correctly.
4. When does the cross product work?
Cross product requires 3D vectors. If you enter two dimensional or higher dimensional vectors, the calculator warns you because the standard cross product needs exactly three components.
5. Why can an inverse fail?
An inverse exists only for square matrices with nonzero determinant. Singular matrices cannot be inverted, so the page returns a message instead of invalid output.
6. What does the graph show?
Vector operations display component or geometric views. Matrix operations display a heatmap of the result or source matrix, helping you inspect structure quickly.
7. What exports are supported?
You can export a simple CSV summary and create a PDF summary of the visible result area. That makes review and sharing easier.
8. Does the calculator show steps for every problem?
Yes. It lists the key operations used to reach the answer. For larger matrices, it summarizes row operations instead of printing every long arithmetic detail.