You have to write a program in C++ to find ONLY the Left Hand Side of this property means `(A + B)^T`.
The following property is true for any two matrices of the same order:
`(A + B)^ T = A^T + B^T `
Here...
- A & B are two matrices of the same order.
- T stands for the transposition of a matrix.
- AT and BT are transposed of matrices A and B respectively.
- The left side of the above equation means:
- Two matrices A and B are added first and then
- The transpose of the resultant is computed.
- The right side means:
- Transpose of both matrices A and B are computed first and then
- Their resultants (transposes) are added.
- Two matrices A and B are added first and then
- The transpose of the resultant is computed.
- Transpose of both matrices A and B are computed first and then
- Their resultants (transposes) are added.
You have to write a program in C++ to find ONLY the Left Hand Side of this property means `(A + B)^T`.
- A two dimensional array named matrix of integers of dimension 2 x 2.
- A setter method setMatrix () which should assign the passed array to the array matrix.
- It should have two constructors:
- A default constructor which should initialize the array matrix to zero.
- A parametrized constructor which should take an array as a parameter and initialize the array matrix with this passed array.
- Here you should call the setMatrix() to do the task.
- An overloaded + operator which should take references to two objects of MatrixProperty and
- Add the two matrices(arrays) of these two objects.
- Return a reference to the resultant matrix.
- A friend function Transpose() which should take one argument:
- a reference to an object of MatrixProperty
- Find transpose of this passed array matrix and
- Return a reference to this resultant matrix.
- A function display() which could either take a reference to an object of MatrixProperty or use this pointer
- To display the passed matrix.
In the main() function, you should:
- Make TWO instances of this class MatrixProperty using the following matrices(arrays).
- Add the above TWO created matrices using the overloaded + operator.
- Call Transpose() function to find transpose of resultant(sum) matrix (done in the above step).
- Call Display() function to:
- display both matrices A and B.
- display the sum(matrix).
- display the transpose(matrix).
Solution:
Program:
#include <iostream>
using namespace std;
class MatrixProperty {
int matrix[2][2];
public:
// Default constructor
MatrixProperty() {
for (int i = 0; i < 2; i++) {
for (int j = 0; j < 2; j++) {
matrix[i][j] = 0;
}
}
}
// Parametrized constructor
MatrixProperty(int temp[2][2]) {
setMatrix(temp);
}
// Setter method
void setMatrix(int temp[2][2]) {
for (int i = 0; i < 2; i++) {
for (int j = 0; j < 2; j++) {
matrix[i][j] = temp[i][j];
}
}
}
// Overloaded + operator
MatrixProperty operator+(MatrixProperty &B) {
MatrixProperty temp;
for (int i = 0; i < 2; i++) {
for (int j = 0; j < 2; j++) {
temp.matrix[i][j] = matrix[i][j] + B.matrix[i][j];
}
}
return temp;
}
// Friend function for transpose
friend MatrixProperty Transpose(MatrixProperty &A) {
MatrixProperty temp;
for (int i = 0; i < 2; i++) {
for (int j = 0; j < 2; j++) {
temp.matrix[i][j] = A.matrix[j][i];
}
}
return temp;
}
// Display function
void display() {
for (int i = 0; i < 2; i++) {
for (int j = 0; j < 2; j++) {
cout << matrix[i][j] << " ";
}
cout << endl;
}
}
};
int main() {
int a[2][2] = {{1, 2}, {3, 4}};
int b[2][2] = {{5, 7}, {6, 2}};
// Create two instances of class MatrixProperty
MatrixProperty A(a);
MatrixProperty B(b);
// Add the matrices using overloaded + operator
MatrixProperty C = A + B;
// Find transpose of sum matrix
MatrixProperty D = Transpose(C);
// Display matrices A and B
cout << "Matrix A:" << endl;
A.display();
cout << "Matrix B:" << endl;
B.display();
// Display sum matrix
cout << "Sum of A and B:" << endl;
C.display();
// Display transpose of sum matrix
cout << "Transpose of sum of A and B:" << endl;
D.display();
return 0;
}
Output:
No comments