Matrix of Minors Calculator

Build any square matrix. Find minors, cofactors, adjugates, exports, and steps. Check matrix structure before advanced algebra work begins.

Calculator

Matrix Entries

Formula Used

For every element aij, remove row i and column j. The determinant of the remaining submatrix is the minor Mij.

Mij = det(A without row i and column j)

Cofactor value is Cij = (-1)i+jMij. The adjugate matrix is the transpose of the cofactor matrix.

How to Use This Calculator

  1. Select a square matrix size from 2 × 2 to 5 × 5.
  2. Enter each matrix value in its matching row and column.
  3. Choose decimal precision for cleaner displayed values.
  4. Select cofactor or adjugate output when needed.
  5. Press calculate to show results above the form.
  6. Use CSV or PDF buttons to save your result.

Example Data Table

Matrix Input Rows Expected Minor Matrix Use Case
3 × 3 3,0,2 / 2,0,-2 / 0,1,1 2,2,2 / -2,3,3 / 0,-10,0 Adjugate practice
2 × 2 4,7 / 2,6 6,2 / 7,4 Basic inverse support
3 × 3 1,2,3 / 0,4,5 / 1,0,6 24,-5,-4 / 12,3,-2 / -2,5,4 Determinant checking

Matrix of Minors Guide

What the Calculator Does

A matrix of minors is a square table built from smaller determinants. Each entry has its own reduced matrix. The calculator removes one row and one column at a time. Then it evaluates the determinant left behind. The result is placed in the same position. This makes the tool useful for algebra, linear systems, and matrix inverses. It also helps students check long handwritten work.

Why Minors Matter

Minors are not only side results. They are the base for cofactors. Cofactors are then used to build the adjugate matrix. The adjugate supports inverse matrix calculations. It also appears in determinant expansion. Because of this, a small sign or arithmetic error can change a final answer. A structured calculator reduces that risk.

Advanced Options

This page accepts matrices from size two to size five. You can type values directly. You can also paste comma separated rows. Decimal precision keeps outputs readable. Optional cofactor and adjugate views extend the result. The original determinant is shown for context. Export buttons help save class notes, reports, or checking records.

Accuracy Notes

Exact integer matrices usually give exact integer minors. Decimal matrices may produce rounded display values. The internal calculation still uses numeric values entered in the form. Use more decimal places when values are sensitive. For symbolic matrices, use manual algebra or a symbolic system. This calculator is designed for numeric Maths work.

Best Practice

First confirm the matrix is square. Next review every row before calculating. Use sample data to understand the layout. Compare the cofactor pattern with alternating signs. Export the final result when you need a permanent copy. With careful input, the matrix of minors becomes much easier to inspect.

FAQs

What is a matrix of minors?

It is a matrix where each entry is the determinant found after removing that entry’s row and column.

Does the calculator support non-square matrices?

No. Minors for this method need square matrices, because each reduced submatrix must have a determinant.

What sizes are supported?

This calculator supports 2 × 2, 3 × 3, 4 × 4, and 5 × 5 square matrices.

Can I calculate cofactors too?

Yes. Enable the cofactor option before submitting. The calculator applies the alternating sign pattern automatically.

What is the adjugate matrix?

The adjugate is the transpose of the cofactor matrix. It is often used when finding matrix inverses.

Can I paste matrix data?

Yes. Paste comma separated rows into the CSV box, then press Import CSV to fill the matrix fields.

Why are some answers rounded?

The decimal precision option controls displayed rounding. Increase precision when working with decimal or sensitive values.

Can I save my result?

Yes. Use the CSV button for spreadsheet data, or use the PDF button for a printable report.

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