Let’s look at the System of Linear Equation with the help of an example:
The input of coefficients and variables is taken into play for consideration.
- The scanner package should be imported into the program in order to use the object of the Scanner class to take the input from the user.
- The array will be initialized to store the variables of the equations.
- The coefficients of the variables will be taken from the user with the help of the object of the Scanner class.
- The equations will then converted into the form of a matrix with the help of a loop.
Two examples are laid off:
- 3 variable linear equations in matrix form.
- N variable linear equations in matrix form.
Illustration: Considering the most used practical linear equation used in mathematics, that is 3 variable linear equations.
Input: ax + by + cz = d Output - 1 2 3 x = 10 5 1 3 y = 12 7 4 2 z = 20
Example 1: Java Program for 3 variable linear equations in matrix form.
// Java Program to Represent Linear Equations in Matrix Form // Importing Scanner class // to take input from user import java.util.Scanner;
public class GFG {
// Mai driver method
public static void main(String args[])
{
// Display message for better readability
System.out.println(
"******** 3 variable linear equation ********" );
// 3 variables of the linear equation
char [] variable = { 'x' , 'y' , 'z' };
// Creating Scanner class object
Scanner sc = new Scanner(System.in);
// Display message for asking user to enter input
System.out.println(
"Enter the coefficients of 3 variable" );
System.out.println(
"Enter in the format shown below" );
System.out.println( "ax + by + cz = d" );
// For 3*3 matrix or in other words
// Dealing with linear equations of 3 coefficients
// Input of coefficients from user
int [][] matrix = new int [ 3 ][ 3 ];
int [][] constt = new int [ 3 ][ 1 ];
// Outer loop for iterating rows
for ( int i = 0 ; i < 3 ; i++) {
// Inner loop for iterating columns
for ( int j = 0 ; j < 3 ; j++) {
// Reading values from usr and
// entering in the matrix form
matrix[i][j] = sc.nextInt();
}
// One row input is over by now
constt[i][ 0 ] = sc.nextInt();
}
// The linear equations in the form of matrix
// Display message
System.out.println(
"Matrix representation of above linear equations is: " );
// Outer loop for iterating rows
for ( int i = 0 ; i < 3 ; i++) {
// Inner loop for iterating columns
for ( int j = 0 ; j < 3 ; j++) {
// Printing matrix corresponding
// linear equation
System.out.print( " " + matrix[i][j]);
}
System.out.print( " " + variable[i]);
System.out.print( " = " + constt[i][ 0 ]);
System.out.println();
}
// Close the stream and release the resources
sc.close();
}
} |
Output:
Now, getting it generic for any value of N: “n-variable linear equation”
Illustration:
Input: ax + by + cz + ... = d Output: 1 2 3 x = 10 5 1 3 y = 12 7 4 2 z = 20 ... ...
Example 2: Java Program for N variable linear equations in matrix form.
import java.util.Scanner;
public class Linear_Equations_n {
public static void main(String args[])
{
System.out.println(
"******** n variable linear equation ********" );
// Initializing the variables
char [] variable
= { 'a' , 'b' , 'c' , 'x' , 'y' , 'z' , 'w' };
System.out.println( "Enter the number of variables" );
Scanner sc = new Scanner(System.in);
int num = sc.nextInt();
System.out.println(
"Enter the coefficients variable" );
System.out.println(
"Enter in the format shown below" );
System.out.println( "ax + by + cz + ... = d" );
// Input of coefficients from user
int [][] matrix = new int [num][num];
int [][] constt = new int [num][ 1 ];
for ( int i = 0 ; i < num; i++) {
for ( int j = 0 ; j < num; j++) {
matrix[i][j] = sc.nextInt();
}
constt[i][ 0 ] = sc.nextInt();
}
// Representation of linear equations in form of
// matrix
System.out.println(
"Matrix representation of above linear equations is: " );
for ( int i = 0 ; i < num; i++) {
for ( int j = 0 ; j < num; j++) {
System.out.print( " " + matrix[i][j]);
}
System.out.print( " " + variable[i]);
System.out.print( " = " + constt[i][ 0 ]);
System.out.println();
}
sc.close();
}
} |
Output –
Time Complexity: O(N2)
Auxiliary Space: O(N2)
The extra space is used to store the elements in the matrix.