Matrix Rank Calculator
Calculate the rank, determinant, and trace of a 2×2 matrix. Determine if the matrix is invertible.
How to Use the Matrix Rank Calculator
- Enter the four elements of the 2×2 matrix.
- Click Calculate to see rank, determinant, and trace.
- The result also shows whether the matrix is invertible.
Referência Rápida
| De | Para |
|---|---|
| [[1,0],[0,1]] | Rank 2, det 1 |
| [[1,2],[2,4]] | Rank 1, det 0 |
| [[0,0],[0,0]] | Rank 0, det 0 |
| det ≠ 0 | Full rank, invertible |
| det = 0 | Singular, not invertible |
Casos de Uso
- •Checking linear independence in linear algebra.
- •Determining if a system of equations has a unique solution.
- •Computing matrix properties for engineering applications.
Fórmula
det = a₁₁·a₂₂ − a₁₂·a₂₁. Rank = 2 if det ≠ 0, rank = 1 if non-zero matrix with det = 0, rank = 0 if zero matrix.
Perguntas Frequentes
What is matrix rank?
The number of linearly independent rows or columns. For a 2×2 matrix, rank is 0, 1, or 2.
When is a matrix invertible?
A square matrix is invertible if and only if its determinant is non-zero.
What is the trace?
The sum of diagonal elements: trace = a₁₁ + a₂₂.