**Source Code:**

#include<stdio.h>#include<math.h>#include<stdlib.h>void matrix_mul(float matrix1[3][3],float matrix2[3][1],float matrix3[3][1]){int i,j,k;for(i = 0; i < 3; i++){for(j = 0; j < 1; j++){matrix3[i][j] = 0;for(k = 0; k < 3; k++){matrix3[i][j] += matrix1[i][k]*matrix2[k][j];}}}}float findmax(float array[3][1]){int i;float maximum;maximum = array[0][0];for(i = 0; i < 3; i++){if(maximum < array[i][0])maximum = array[i][0];}return maximum;}int isEqual(float matrix1[3][1], float matrix2[3][1]){if(matrix1[0][0] == matrix2[0][0]&& matrix1[1][0] == matrix2[1][0]&& matrix1[2][0] == matrix2[2][0])return 1;return 0;}int main(){float matrix1[3][3], matrix2[3][1],result[3][1];float eigenValue;int i,j,k;printf("Enter 3x3 matrix:\n");for(i = 0; i < 3; i++){for(j = 0; j < 3; j++){scanf("%f",&matrix1[i][j]);}}for(i = 0; i < 3; i++){for(j = 0; j < 1; j++){matrix2[i][j] = 1.0;}}while(1){matrix_mul(matrix1,matrix2,result);eigenValue = findmax(result);for(i = 0; i < 3; i++){result[i][0]/=eigenValue;}if(isEqual(matrix2,result)==1){break;}for(i = 0; i < 3; i++){matrix2[i][0] = result[i][0];}}printf("Greatest Eigen Value = %f", eigenValue);printf("\nAny one of Eigen Vector: \n");for(i = 0; i < 3; i++){for(j = 0; j < 1; j++){printf("%.2f",result[i][j]);printf("\t");}printf("\n");}return 0;}

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