CALCULATE WITH CONFIDENCE

Linear Algebra & Matrices

Linear Independence Calculator

Test exact linear independence of vectors entered as matrix columns.

Linear Algebra & Matrices

Enter matrix values

Exact structural results; labelled numerical approximations where required
Vectors as columns of A

Use signed finite decimals. Fill every visible cell. Fractions, commas, and scientific notation are not accepted.

Linear algebra result

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Enter valid values to see the result.

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Quick guide

How to use this calculator

  1. Set the matrix dimensions required by the task.
  2. Fill every visible entry and any operation-specific control.
  3. Read the result type, factors, classification, and disclosed limitations.

Calculation method

Apply the stated linear-algebra contract

Columns are independent exactly when rank(A) equals the number of columns.

Undefined, singular, dimensionally incompatible, dependent, or unsupported inputs receive an explicit message instead of a fabricated numeric result.

Worked example

Example interpretation

A nontrivial null-space direction proves dependence.

Columns are independent exactly when rank(A) equals the number of columns.

Supported inputs

Precision and limits

Matrix size

Input matrices are limited to 1–6 rows and columns; operation-specific square, rank, or compatibility rules still apply.

Entry precision

Enter signed finite decimals with at most 30 digits and 15 decimal places.

Exactness

Finite decimals become reduced rational numbers and intermediate structural calculations are not rounded.