Multiply a Matrix by a Vector
Matrix-column vector multiplication. Runs entirely in your browser, so your data never leaves your device.
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Output
The result appears here as you type.
How to use Multiply a Matrix by a Vector
- 1. Paste the matrix and vector. Enter the matrix rows first, then a blank line, then the column vector on its own line, for example (1, 2, 3). The vector's length must match the matrix's column count.
- 2. Read what the tool computes. The tool multiplies the matrix by the column vector, producing a new vector where each entry is the dot product of one matrix row with the input vector.
- 3. Copy the resulting vector. The output vector appears in parentheses format in the output pane. Copy it into your homework, linear algebra script, or further matrix calculation.
When to use Multiply a Matrix by a Vector
Multiply a Matrix by a Vector applies a linear transformation to a column vector, the operation at the heart of linear algebra. Use it to see the result of A times x without setting up the row-by-row dot products yourself.
- Applying a linear transformation. You built a transformation matrix for rotation, scaling, or projection in a graphics assignment and want to see exactly where it sends a specific input vector before coding the transform.
- Checking a system of linear equations. Given a coefficient matrix and a candidate solution vector, multiplying them lets you verify whether the solution actually satisfies Ax = b by comparing the result to the expected right-hand side.
- Verifying a homework calculation. A linear algebra course has you compute a matrix-vector product by hand as practice, and you want a quick way to check your arithmetic before submitting the assignment.
- Understanding a Markov chain transition step. A probability exercise models one step of a Markov chain as a transition matrix times a state vector, and computing the product shows the next state distribution directly.
Examples
Enter the matrix, a blank line, then the vector on one line
Input
1 2 3 4 5 6 (1, 2, 3)
Output
(14, 32)
About the Multiply a Matrix by a Vector tool
Multiply a Matrix by a Vector does its work locally, right in the browser. Matrix-column vector multiplication. There is no upload step, no queue and no account, and your data never travels over the network.
It belongs to the Math Tools collection on EditSafely, a set of 234 small, focused Math utilities that share the same instant, private workspace.
There is nothing to configure. Provide the input and the result appears on its own. A worked example further down the page shows exactly what the tool produces for a real input.
Running locally also makes the tool fast and dependable: results appear as you type or drop a file, there is no server outage that can take it down mid-task, and confidential data can be processed without a second thought.
Frequently asked questions
Is Multiply a Matrix by a Vector free to use?
Yes, it is completely free. All 2,658 tools on EditSafely work without an account, a subscription or usage limits.
Is it safe to paste sensitive or confidential data?
Everything happens locally. Your browser downloads the tool's code once, then does all the processing itself; nothing you enter is transmitted, stored or logged. You can even go offline after the page loads and it will still work.
How much text can I process at once?
There is no fixed limit. Because the work happens on your own device rather than on a shared server, the practical ceiling is your machine's memory, which comfortably handles inputs far larger than typical online tools allow.
Do I need to sign up or install anything?
No. The tool works in any modern browser on desktop, tablet or phone. There is no account to create, no extension to add and no software to install.
How do I use the result?
The output panel has a one-click copy button, and you can keep refining the input while you work; the result updates in place as you type.