21-06-2024 07:40

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Tags : mathematics Matrix linear algebra Linear Equations

Rank of matrix

Let A be a non-zero matrix. A positive integer r is called the rank of the matrix A if

• Every minor of order greater than r is zero.
• There exists at least one minor of order r which is non-zero, and

the rank of matrix A is denoted by ρ(A). The rank in echelon form is equal to the number of non-zero rows of the matrix.

Methods to find (determine) the rank of a matrix:

1. Minor (Determinant) form
2. Echelon Form

References