Question #23152

In the programming language of your choice write a function which determines if a 3x3 matrix is non-singular. Use remark statements to explain how the program works. You may want to use your calculator’s programming language.

Expert's answer

#include <conio.h>

#include <iomanip>

#include <iostream>

using namespace std;

int find_determinant(int (&matrix)[3][3])

{

int result = 0;

result += matrix[0][0] * matrix[1][1] * matrix[2][2];

result += matrix[0][1] * matrix[1][2] * matrix[2][0];

result += matrix[1][0] * matrix[2][1] * matrix[0][2];

result -= matrix[0][2] * matrix[1][1] * matrix[2][0];

result -= matrix[1][0] * matrix[0][1] * matrix[2][2];

result -= matrix[2][1] * matrix[1][2] * matrix[0][0];

return result;

}

void main()

{

/* Initialize a 3x3 matrix */

int matrix[3][3] = { {8, 0, 5},

{2, 4, 0},

{1, 7, 3} };

/* Display the matrix */

for (int x = 0; x < 3; x++)

{

for (int y = 0; y < 3; y++)

cout << setw(3) << matrix[x][y];

cout << endl;

}

cout << endl;

/* Check if it's determinant is equal to 0 */

if (find_determinant(matrix) == 0)

cout << "This matrix isn't invertible." << endl;

else

cout << "This matrix is non-singular." << endl;

_getch();

}

#include <iomanip>

#include <iostream>

using namespace std;

int find_determinant(int (&matrix)[3][3])

{

int result = 0;

result += matrix[0][0] * matrix[1][1] * matrix[2][2];

result += matrix[0][1] * matrix[1][2] * matrix[2][0];

result += matrix[1][0] * matrix[2][1] * matrix[0][2];

result -= matrix[0][2] * matrix[1][1] * matrix[2][0];

result -= matrix[1][0] * matrix[0][1] * matrix[2][2];

result -= matrix[2][1] * matrix[1][2] * matrix[0][0];

return result;

}

void main()

{

/* Initialize a 3x3 matrix */

int matrix[3][3] = { {8, 0, 5},

{2, 4, 0},

{1, 7, 3} };

/* Display the matrix */

for (int x = 0; x < 3; x++)

{

for (int y = 0; y < 3; y++)

cout << setw(3) << matrix[x][y];

cout << endl;

}

cout << endl;

/* Check if it's determinant is equal to 0 */

if (find_determinant(matrix) == 0)

cout << "This matrix isn't invertible." << endl;

else

cout << "This matrix is non-singular." << endl;

_getch();

}

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