Matrix Adjugate 4x4 Calculator

Enter sixteen values and compute the adjugate accurately. Inspect cofactor signs, determinant checks, and symmetry. Download clean outputs for classes, audits, projects, and homework.

Calculator Input

Use the responsive cards below to enter all sixteen matrix values. Large screens show three cards per row, medium screens show two, and mobile screens show one.

Matrix Row 1

Matrix Row 2

Matrix Row 3

Matrix Row 4

Options

Included outputs
  • Determinant
  • Cofactor matrix
  • Adjugate matrix
  • Inverse preview when valid
  • CSV and PDF export
  • Adjugate heatmap

Actions

Example data is preselected on first load. You can replace any entry with integers, decimals, or negative values.

Example Data Table

Example Row 1 Row 2 Row 3 Row 4 Determinant Adjugate R1
Sample A [2, 1, 0, -1] [3, 2, 1, 4] [1, 0, 2, 5] [0, 1, -2, 3] 20 [29, -18, 16, 7]

This sample matrix is invertible because its determinant is nonzero. It is useful for checking your manual cofactor and transpose work.

Formula Used

Minor matrix: Mij is formed by deleting row i and column j.

Cofactor: Cij = (-1)i+j × det(Mij)

Adjugate: adj(A) = CT

Inverse when valid: A-1 = adj(A) / det(A), only when det(A) ≠ 0.

Cofactor sign pattern for 4×4 matrices
+-+-
-+-+
+-+-
-+-+

The calculator evaluates sixteen 3×3 minors, applies alternating cofactor signs, assembles the cofactor matrix, and then transposes that matrix to produce the adjugate.

How to Use This Calculator

  1. Enter all sixteen values of your 4×4 matrix.
  2. Select the number of decimal places you want.
  3. Click Calculate Adjugate.
  4. Review the determinant, cofactor matrix, and adjugate matrix.
  5. Check the inverse preview when the determinant is nonzero.
  6. Use the CSV or PDF buttons to export the result.
  7. Use the heatmap to inspect large positive or negative adjugate entries quickly.

FAQs

1) What is an adjugate matrix?

The adjugate is the transpose of a matrix’s cofactor matrix. It is commonly used to build the inverse when the determinant is nonzero.

2) Does the adjugate exist when the determinant is zero?

Yes. The adjugate always exists for a square matrix. Only the inverse fails when the determinant equals zero.

3) Why are cofactors signed positively and negatively?

Cofactors follow an alternating sign pattern. This pattern preserves correct determinant expansion and ensures the adjugate is mathematically consistent.

4) What does this calculator display after submission?

It shows the determinant, the cofactor matrix, the adjugate matrix, an inverse preview when valid, plus export buttons and a heatmap.

5) Can I use decimals and negative values?

Yes. The inputs accept integers, decimals, and negative values, so the calculator works for many practical algebra and engineering exercises.

6) Why is the result shown above the form?

The page is designed to place the computed output directly below the header. This makes the final matrices visible immediately after submission.

7) What does the Plotly graph show?

The graph is a heatmap of adjugate values. Large positive and negative entries stand out visually, helping with fast interpretation and verification.

8) How can I verify a result manually?

Compute each 3×3 minor, apply the cofactor sign pattern, build the cofactor matrix, then transpose it. Compare those values with the calculator output.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.