Create FindTheRankOfAMatrix.swift (#5620)

Implemented a function that reduces the matrix to its row echelon form and counts the number of pivot elements (non-zero leading elements in each row). The rank of the matrix is equal to the number of these pivot elements.

Co-authored-by: Ritesh Kokam <61982298+RiteshK-611@users.noreply.github.com>

program/program/find-the-rank-of-a-matrix/FindTheRankOfAMatrix.swift

@@ -0,0 +1,44 @@
+import Foundation
+
+func findRankOfMatrix(_ matrix: [[Double]]) -> Int {
+    var mat = matrix
+    let rowCount = mat.count
+    let colCount = mat[0].count
+    var rank = 0
+
+    for row in 0..<colCount {
+        if row < rowCount {
+            var swapRow = row
+            while mat[swapRow][row] == 0 {
+                swapRow += 1
+                if swapRow == rowCount {
+                    swapRow = row
+                    break
+                }
+            }
+            mat.swapAt(row, swapRow)
+
+            if mat[row][row] != 0 {
+                for i in (row+1)..<rowCount {
+                    let factor = mat[i][row] / mat[row][row]
+                    for j in row..<colCount {
+                        mat[i][j] -= factor * mat[row][j]
+                    }
+                }
+                rank += 1
+            }
+        }
+    }
+
+    return rank
+}
+
+// Example usage
+let matrix = [
+    [1.0, 2.0, 3.0],
+    [4.0, 5.0, 6.0],
+    [7.0, 8.0, 9.0]
+]
+
+let rank = findRankOfMatrix(matrix)
+print("Rank of the matrix: \(rank)")