Calculator
Formula Used
Matrix-vector product: y = A × x
Dimension rule: (m × n) × (n × 1) = (m × 1)
Component formula: yi = Σ aijxj, for j = 1 to n
Each result component comes from one matrix row dotted with the vector.
The calculator also shows each row expression, the final output vector, summary values, and a Plotly bar chart for quick interpretation.
How to Use This Calculator
- Choose the number of matrix rows and columns.
- Enter the matrix values in the grid or paste them into the bulk box.
- Enter the vector values. Its length must match the matrix column count.
- Select decimal precision and output display style.
- Press the calculate button to show the result above the form.
- Review row-by-row dot products, summary figures, and the graph.
- Download the result as CSV or PDF when needed.
Example Data Table
| Row | Matrix Row | Vector | Computation | Result |
|---|---|---|---|---|
| 1 | [2, 1, -1] | [3, 1, 2] | (2×3) + (1×1) + (-1×2) | 5 |
| 2 | [1, 3, 2] | [3, 1, 2] | (1×3) + (3×1) + (2×2) | 10 |
| 3 | [0, -2, 4] | [3, 1, 2] | (0×3) + (-2×1) + (4×2) | 6 |
Example output vector: y = [5, 10, 6]T
Frequently Asked Questions
1. What dimensions are required for multiplication?
The matrix must have n columns, and the vector must contain n entries. If the counts do not match, multiplication is not defined.
2. Can I enter decimals, negatives, or zeros?
Yes. The calculator accepts decimal values, negative numbers, and zeros in both the matrix and the vector.
3. What does each output value mean?
Each output component is the dot product of one matrix row with the input vector. One row creates one result entry.
4. Why is my result not appearing?
This usually means one or more entries are empty, non-numeric, or the vector length does not match the matrix column count.
5. What is the graph showing?
The Plotly chart displays output vector components as bars. It helps you compare magnitudes and identify large positive or negative entries quickly.
6. When should I use trimmed or fixed decimals?
Use trimmed decimals for cleaner reading. Use fixed decimals when you need consistent formatting for reports, classwork, or copied tables.
7. What is included in the CSV and PDF exports?
Exports include the matrix, vector, output vector, and the row-by-row multiplication breakdown so you can save or share your work.
8. Can this help me verify homework steps?
Yes. The row expressions show how every component is formed, making it useful for checking manual calculations and spotting entry mistakes.