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# Java Program to check for Lower Triangular Matrix

#### Question:

Write a Program in Java to input a 2-D square matrix and check whether it is a Lower Triangular Matrix or not.

Lower Triangular Matrix : A Lower Triangular matrix is a square matrix in which all the entries above the main diagonal (↘) are zero. The entries below or on the main diagonal themselves may or may not be zero.

Example:

$\begin{bmatrix} 5 & 0 & 0 & 0 \\ 3 & 1 & 0 & 0 \\ 4 & 9 & 4 & 0 \\ 6 & 8 & 7 & 2 \end{bmatrix}$

#### Solution:

/**
* The class LowerTriangularMatrix inputs a Matrix and checks whether it is a Lower Triangular Matrix or not
* @author : www.guideforschool.com
* @Program Type : BlueJ Program - Java
*/

import java.util.*;
class LowerTriangularMatrix
{
public static void main(String args[])throws Exception
{
Scanner sc=new Scanner(System.in);
System.out.print("Enter the size of the matrix : ");
int m=sc.nextInt();
int A[][]=new int[m][m];

/* Inputting the matrix */
for(int i=0;i<m;i++)
{
for(int j=0;j<m;j++)
{
System.out.print("Enter an element : ");
A[i][j]=sc.nextInt();
}
}

/* Printing the matrix */
System.out.println("*************************");
System.out.println("The Matrix is : ");
for(int i=0;i<m;i++)
{
for(int j=0;j<m;j++)
{
System.out.print(A[i][j]+"\t");
}
System.out.println();
}
System.out.println("*************************");

int p=0;

for(int i=0;i<m;i++)
{
for(int j=i+1;j<m;j++)
{
/* Checking that the matrix is Lower Triangular or not */
if(A[i][j]!=0) // All elements above the diagonal must be zero
{
p=1;
break;
}
}
}

if(p==0)
System.out.println("The matrix is Lower Triangular");
else
System.out.println("The matrix is not Lower Triangular");
}
}

#### Output:

Enter the size of the matrix : 4
Enter an element : 5
Enter an element : 0
Enter an element : 0
Enter an element : 0
Enter an element : 3
Enter an element : 1
Enter an element : 0
Enter an element : 0
Enter an element : 4
Enter an element : 9
Enter an element : 4
Enter an element : 0
Enter an element : 6
Enter an element : 8
Enter an element : 7
Enter an element : 2
*************************
The Matrix is :
5 0 0 0
3 1 0 0
4 9 4 0
6 8 7 2
*************************
The matrix is Lower Triangular

## ISC 2017 Computer Science Solution + Examiner’s Comments – From the Council

Solution of ISC 2017 Computer science Paper as provided by the Council for the Indian School Certificate Examinations.