Matrix:

Matrix Rank:

Steps to Calculate Rank:

  1. Identify the matrix dimensions (rows x columns).
  2. Apply Gaussian elimination. Check if the pivot is non-zero; if not, swap rows.
  3. For each row, eliminate the values below the pivot using row operations.
  4. Continue the row operations until the matrix is in row echelon form.
  5. Count the number of non-zero rows; this is the rank of the matrix.