What is Upper Triangular Matrix? An **upper triangular matrix** is a **square matrix** in which all the **elements below the diagonal** are **zero**. We consider a Matrix U with ‘i’ rows and ‘j’ columns, then **mathematically** we **represent** the upper triangular matrix as

In another word strictly upper triangular matrix is an **upper triangular matrix having 0’s along the diagonal** as well, i.e., U(ij)=0 for i>=j.

- Program in C
#include <stdio.h> #include <stdlib.h> int main() { int **m, o, i , j; printf("Enter the order of matrix:"); // the order of the matrix from user scanf("%d", &o); m = (int **)malloc(sizeof (int) * o); // dynamically allocate memory to store entries for (i = 0; i < o; i++) { m[i] = (int *)malloc(sizeof (int) * o); } printf("Enter your inputs:n"); // get the input matrix from the user for (i = 0; i < o; i++) { for (j = 0; j < o; j++) { scanf("%d", &m[i][j]); } } for (i = 0; i < o; i++) // check for upper triangulat matrix { for (j = i - 1; j >= 0; j--) { if (m[i][j] != 0) { printf("Not an upper triangular matrixn"); exit(0); } } } printf("Given matrix is an upper triangular matrixn"); // print the output of upper matrix return 0; }

**Output:**Output 1:

Enter the order of matrix:3

Enter your inputs:

1 2 3

0 4 5

0 0 9

Given matrix is an upper triangular matrixOutput 2:

Enter the order of matrix:3

Enter your inputs:

1 2 3

0 4 5

7 0 9

Not an upper triangular matrix - Program in java
import java.util.*; class UpperTriangularMatrix { public static void main(String args[])throws Exception { Scanner sy=new Scanner(System.in); System.out.print("Enter the order of the matrix : "); //get order of matrix int n=sy.nextInt(); int Arr[][]=new int[n][n]; for(int i=0;i<n;i++) // get Input in the matrix { for(int j=0;j<n;j++) { System.out.print("Enter an element : "); Arr[i][j]=sy.nextInt(); } } System.out.println("____________________"); // Print the matrix System.out.println("The Matrix you enter is : "); for(int i=0;i<n;i++) { for(int j=0;j<n;j++) { System.out.print(Arr[i][j]+"t"); } System.out.println(); } System.out.println("_____________________"); int k=0; for(int i=0;i<n;i++) // Check the matrix is Upper Triangular Matrix or not { for(int j=0;j<i;j++) { if(Arr[i][j]!=0) // All elements below the diagonal must be zero { p=1; break; } } } if(p==0) System.out.println("The matrix is an Upper Triangular Matrix"); else System.out.println("The matrix is not an Upper Triangular Matrix"); } }

**Output:**Enter the order of the matrix : 4

Enter an element : 1

Enter an element : 2

Enter an element : 3

Enter an element : 4

Enter an element : 0

Enter an element : 6

Enter an element : 7

Enter an element : 8

Enter an element : 0

Enter an element : 0

Enter an element : 2

Enter an element : 3

Enter an element : 0

Enter an element : 0

Enter an element : 0

Enter an element : 7

_____________________

The Matrix is :

1 2 3 4

0 6 7 8

0 0 2 3

0 0 0 7

_____________________

The matrix is an Upper Triangular Matrix