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A row matrix is a matrix that consists of a single row and multiple columns. It is typically represented as a 1 x n matrix, where "n" is the number of columns. Row matrices are often used in linear algebra to represent vectors in a horizontal orientation, and they can be involved in various operations such as matrix multiplication and addition.
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C program to perform addition of matrices using functions?
#include<iostream> #include<iomanip> #include<vector> #include<string> #include<sstream> using namespace std; const unsigned width = 4; const unsigned height = 3; class matrix { private: vector< vector<unsigned> > m_data; string m_title; public: matrix(string title=""): m_data(height, vector<unsigned>(width)), m_title(title) {} matrix(const matrix& copy): m_data(copy.m_data), m_title(copy.m_title) {} matrix& operator=(matrix rhs) { // Note: assignment does not overwrite the matrix title. for(unsigned row=0; row<height; ++row) for(unsigned col=0; col<width; ++col) operator[](row)[col]=rhs[row][col]; return(*this); } vector<unsigned>& operator[](const unsigned index){return(m_data[index]);} void set_title(const string title){ m_title = title; } string& get_title(){return(m_title);} void show() { cout<<m_title<<'\n'<<endl; for(unsigned row=0; row<height; ++row) { for(unsigned col=0; col<width; ++col) cout<<setw(7)<<(*this)[row][col]; cout<<endl; } cout<<endl; } matrix& operator+=(matrix rhs) { for(unsigned row=0; row<height; ++row) for(unsigned col=0; col<width; ++col) (*this)[row][col]+=rhs[row][col]; return(*this); } matrix operator+(matrix rhs) { matrix result(m_title+" + "+rhs.m_title); for(unsigned row=0; row<height; ++row) for(unsigned col=0; col<width; ++col) result[row][col]=(*this)[row][col]+rhs[row][col]; return(result); } matrix& operator-=(matrix rhs) { for(unsigned row=0; row<height; ++row) for(unsigned col=0; col<width; ++col) (*this)[row][col]-=rhs[row][col]; return(*this); } matrix operator-(matrix rhs) { matrix result(m_title+" - "+rhs.m_title); for(unsigned row=0; row<height; ++row) for(unsigned col=0; col<width; ++col) result[row][col]=operator[](row)[col]-rhs[row][col]; return(result); } }; unsigned input_num (std::string prompt) { unsigned id = 0; while (1) { cout<<prompt<<": "; string input=""; getline (cin, input); stringstream ss (input); if (ss>>id) break; cout<<"Invalid input.\n"; } return (id); } void initialise(matrix& m) { for(unsigned row=0; row<height; ++row) { for(unsigned col=0; col<width; ++col) { stringstream ss; ss<<"Enter a value for "<<m.get_title()<<'['<<row<<"]["<<col<<']'; m[row][col]=input_num(ss.str()); } } cout<<endl; } int main() { matrix matrix_1("matrix_1"); initialise(matrix_1); matrix_1.show(); matrix matrix_2("matrix_2"); initialise(matrix_2); matrix_2.show(); matrix matrix_3 = matrix_1 + matrix_2; matrix_3.show(); matrix matrix_4 = matrix_3 - matrix_2; matrix_4.show(); }
Perform addition multiplication subtraction of 2-D array using Operator Overloading in C plus plus?
#include<iostream> #include<vector> #include<random> template<const size_t R, const size_t C> class Matrix { public: using row_type = int[C]; private: // attributes int m_data[R][C]; public: // construction/assignment Matrix (); Matrix (const Matrix& source); Matrix (Matrix&& source); Matrix& operator= (const Matrix<R,C>& source); Matrix& operator= (Matrix<R,C>&& source); ~Matrix () {} public: // accessors row_type& row (const size_t index) { return m_data[index]; } const row_type& row (const size_t index) const { return m_data[index]; } row_type& operator[] (const size_t index) { return m_data[index]; } const row_type& operator[] (const size_t index) const { return m_data[index]; } size_t size() const { return R * C; } size_t rows() const { return R; } size_t cols() const { return C; } public: // operations Matrix<R,C>& operator+= (const Matrix<R,C>&); Matrix<R,C>& operator-= (const Matrix<R,C>&); }; template<const size_t R, const size_t C> Matrix<R,C>::Matrix() { for (size_t row=0; row<R; ++row) for (size_t col=0; col<C; ++col) m_data[row][col] = 0; } template<const size_t R, const size_t C> Matrix<R,C>::Matrix(const Matrix<R,C>& source) { for (size_t row=0; row<R; ++row) for (size_t col=0; col<C; ++col) m_data[row][col] = source.m_data[row][col]; } template<const size_t R, const size_t C> Matrix<R,C>::Matrix(Matrix<R,C>&& source) { for (size_t row=0; row<R; ++row) for (size_t col=0; col<C; ++col) m_data[row][col] = std::move (source.m_data[row][col]); } template<const size_t R, const size_t C> Matrix<R,C>& Matrix<R,C>::operator= (const Matrix<R,C>& source) { for (size_t row=0; row<R; ++row) for (size_t col=0; col<C; ++col) m_data[row][col] = source.m_data[row][col]; return *this; } template<const size_t R, const size_t C> Matrix<R,C>& Matrix<R,C>::operator= (Matrix<R,C>&& source) { for (size_t row=0; row<R; ++row) for (size_t col=0; col<C; ++col) m_data[row][col] = std::move (source.m_data[row][col]); return *this; } template<const size_t R, const size_t C> Matrix<R,C>& Matrix<R,C>::operator+= (const Matrix<R,C>& rhs) { for (size_t row=0; row<R; ++row) for (size_t col=0; col<C; ++col) m_data[row][col] += rhs.m_data[row][col]; return *this; } template<const size_t R, const size_t C> Matrix<R,C>& Matrix<R,C>::operator-= (const Matrix<R,C>& rhs) { for (size_t row=0; row<R; ++row) for (size_t col=0; col<C; ++col) m_data[row][col] -= rhs.m_data[row][col]; return *this; } template<const size_t R, const size_t C> Matrix<R,C> operator+ (const Matrix<R,C>& lhs, const Matrix<R,C>& rhs) { Matrix<R,C> sum (lhs); return sum += rhs; } template<const size_t R, const size_t C> Matrix<R,C> operator- (const Matrix<R,C>& lhs, const Matrix<R,C>& rhs) { Matrix<R,C> sub (lhs); return sub -= rhs; } template<const size_t R, const size_t C, const size_t R1, const size_t C1> Matrix<R,C1> operator* (const Matrix<R,C>& lhs, const Matrix<R1,C1>& rhs) { static_assert (C==R1, "Matrix dimension mismatch!"); Matrix<R,C1> mul; for (size_t x=0; x!=R; ++x) { for (size_t y=0; y!=C1; ++y) { int prod = 0; for (size_t z=0; z!=C; ++z) { prod += lhs[x][z] * rhs[z][y]; } mul[x][y] = prod; } } return mul; } template<const size_t R, const size_t C> std::ostream& operator<< (std::ostream& os, const Matrix<R,C>& m) { for (size_t row=0; row<R; ++row) { for (size_t col=0; col<C; ++col) { std::cout << m[row][col] << '\t'; } std::cout << std::endl; } return os; } int main() { std::default_random_engine generator; std::uniform_int_distribution<int> distribution (1,9); const size_t rows = 2; const size_t cols = 3; Matrix<rows, cols> a, b; for (size_t row=0; row<rows; ++row) { for (size_t col=0; col<cols; ++col) { a[row][col] = distribution (generator); b[row][col] = distribution (generator); } } std::cout << "Matrix a:\n\n" << a << '\n' << std::endl; std::cout << "Matrix b:\n\n" << b << '\n' << std::endl; std::cout << "Matrix a + b:\n\n" << a + b << '\n' << std::endl; std::cout << "Matrix a - b:\n\n" << a - b << '\n' << std::endl; Matrix<cols, rows> c; for (size_t row=0; row<rows; ++row) { for (size_t col=0; col<cols; ++col) { c[col][row] = distribution (generator); } } std::cout << "Matrix c:\n\n" << c << '\n' << std::endl; std::cout << "Matrix a * c:\n\n" << a * c << '\n' << std::endl; }
Write a c plus plus program to add two matrix using arrays?
Matrix Add/* Program MAT_ADD.C**** Illustrates how to add two 3X3 matrices.**** Peter H. Anderson, Feb 21, '97*/#include <stdio.h>void add_matrices(int a[][3], int b[][3], int result[][3]);void print_matrix(int a[][3]);void main(void){int p[3][3] = { {1, 3, -4}, {1, 1, -2}, {-1, -2, 5} };int q[3][3] = { {8, 3, 0}, {3, 10, 2}, {0, 2, 6} };int r[3][3];add_matrices(p, q, r);printf("\nMatrix 1:\n");print_matrix(p);printf("\nMatrix 2:\n");print_matrix(q);printf("\nResult:\n");print_matrix(r);}void add_matrices(int a[][3], int b[][3], int result[][3]){int i, j;for(i=0; i<3; i++){for(j=0; j<3; j++){result[i][j] = a[i][j] + b[i][j];}}}void print_matrix(int a[][3]){int i, j;for (i=0; i<3; i++){for (j=0; j<3; j++){printf("%d\t", a[i][j]);}printf("\n");}}
How to write a c plus plus program to multiply matrices using function template?
#include<iostream> #include<algorithm> #include<cassert> unsigned multiply_recursive (unsigned a, unsigned b) { if (!a !b) return 0; // Note: not(a) or not (b) if (a==1) return b; if (b==1) return a; return a + multiply_recursive (a, --b); } unsigned multiply_iterative (unsigned a, unsigned b) { int product = 0; int x = std::min (a, b); int y = std::max (b, a); while (x--) product += y; return product; } int main() { unsigned x, y; // Test all combinations with 0. x = multiply_recursive (0, 0); assert (x==0); x = multiply_iterative (0, 0); assert (x==0); x = multiply_recursive (0, 1); assert (x==0); x = multiply_iterative (0, 1); assert (x==0); x = multiply_recursive (1, 0); assert (x==0); x = multiply_iterative (1, 0); assert (x==0); // Test non-zero values with 1. x = multiply_recursive (1, 42); // inefficient: lowest value must be on right (fewer recursions). y = multiply_iterative (1, 42); assert (x==42 && y==42); x = multiply_recursive (42, 1); y = multiply_iterative (42, 1); assert (x==42 && y==42); // Test other non-zero values are commutative. x = multiply_recursive (24, 42); // inefficient: lowest value must be on right (fewer recursions). y = multiply_iterative (24, 42); assert (x==1008 && y==1008); x = multiply_recursive (42, 24); y = multiply_iterative (42, 24); assert (x==1008 && y==1008); }
How do you generate the for loop in matrix?
To generate a for loop in a matrix, you typically iterate over the rows and columns of the matrix using nested loops. The outer loop iterates through each row, while the inner loop iterates through each column within that row. For example, in Python, you could use for i in range(rows): for the outer loop and for j in range(columns): for the inner loop. This allows you to access each element of the matrix using the indices matrix[i][j].
Why matrix multipliucation is possible by row vs column?
Matrix multiplication is possible by row versus column because it involves taking the dot product of the rows of the first matrix with the columns of the second matrix. Each element of the resulting matrix is computed by summing the products of corresponding entries from a row of the first matrix and a column of the second matrix. This operation aligns with the definition of matrix multiplication, where the number of columns in the first matrix must equal the number of rows in the second matrix. Thus, the row-column pairing enables systematic computation of the resulting matrix's elements.
What is a reduced matrix?
Reduced matrix is a matrix where the elements of the matrix is reduced by eliminating the elements in the row which its aim is to make an identity matrix.
What are the elementry matrices?
An elementary matrix is a matrix obtained from the identity matrix following one of the following row operations:Swap 2 rows;Multiply any row by a non-zero constant;Replace a row by the sum of itself and a non-zero multiple of another row.
How can I use MATLAB to view a specific value in a sparse matrix?
To view a specific value in a sparse matrix using MATLAB, you can use the command full(matrix(row, column)) where matrix is your sparse matrix and row and column are the indices of the value you want to view. This command converts the sparse matrix to a full matrix and allows you to access the specific value at the given row and column.
C program to perform addition of matrices using functions?
#include<iostream> #include<iomanip> #include<vector> #include<string> #include<sstream> using namespace std; const unsigned width = 4; const unsigned height = 3; class matrix { private: vector< vector<unsigned> > m_data; string m_title; public: matrix(string title=""): m_data(height, vector<unsigned>(width)), m_title(title) {} matrix(const matrix& copy): m_data(copy.m_data), m_title(copy.m_title) {} matrix& operator=(matrix rhs) { // Note: assignment does not overwrite the matrix title. for(unsigned row=0; row<height; ++row) for(unsigned col=0; col<width; ++col) operator[](row)[col]=rhs[row][col]; return(*this); } vector<unsigned>& operator[](const unsigned index){return(m_data[index]);} void set_title(const string title){ m_title = title; } string& get_title(){return(m_title);} void show() { cout<<m_title<<'\n'<<endl; for(unsigned row=0; row<height; ++row) { for(unsigned col=0; col<width; ++col) cout<<setw(7)<<(*this)[row][col]; cout<<endl; } cout<<endl; } matrix& operator+=(matrix rhs) { for(unsigned row=0; row<height; ++row) for(unsigned col=0; col<width; ++col) (*this)[row][col]+=rhs[row][col]; return(*this); } matrix operator+(matrix rhs) { matrix result(m_title+" + "+rhs.m_title); for(unsigned row=0; row<height; ++row) for(unsigned col=0; col<width; ++col) result[row][col]=(*this)[row][col]+rhs[row][col]; return(result); } matrix& operator-=(matrix rhs) { for(unsigned row=0; row<height; ++row) for(unsigned col=0; col<width; ++col) (*this)[row][col]-=rhs[row][col]; return(*this); } matrix operator-(matrix rhs) { matrix result(m_title+" - "+rhs.m_title); for(unsigned row=0; row<height; ++row) for(unsigned col=0; col<width; ++col) result[row][col]=operator[](row)[col]-rhs[row][col]; return(result); } }; unsigned input_num (std::string prompt) { unsigned id = 0; while (1) { cout<<prompt<<": "; string input=""; getline (cin, input); stringstream ss (input); if (ss>>id) break; cout<<"Invalid input.\n"; } return (id); } void initialise(matrix& m) { for(unsigned row=0; row<height; ++row) { for(unsigned col=0; col<width; ++col) { stringstream ss; ss<<"Enter a value for "<<m.get_title()<<'['<<row<<"]["<<col<<']'; m[row][col]=input_num(ss.str()); } } cout<<endl; } int main() { matrix matrix_1("matrix_1"); initialise(matrix_1); matrix_1.show(); matrix matrix_2("matrix_2"); initialise(matrix_2); matrix_2.show(); matrix matrix_3 = matrix_1 + matrix_2; matrix_3.show(); matrix matrix_4 = matrix_3 - matrix_2; matrix_4.show(); }
How to construct a matrix with 23 elements?
It will either be a 1*23 row matrix or a 23*1 column matrix.
Write a c plus plus program that calculate the matrix of three by three addition?
#include<iostream> #include<vector> #include<time.h> template<const size_t R, const size_t C> class Matrix { public: using row_type = int[C]; private: // attributes int m_data[R][C]; public: // construction/assignment Matrix (); Matrix (const Matrix& source); Matrix (Matrix&& source); Matrix& operator= (const Matrix<R,C>& source); Matrix& operator= (Matrix<R,C>&& source); ~Matrix () {} public: // accessors row_type& row (const size_t index) { return m_data[index]; } const row_type& row (const size_t index) const { return m_data[index]; } row_type& operator[] (const size_t index) { return m_data[index]; } const row_type& operator[] (const size_t index) const { return m_data[index]; } size_t size() const { return R * C; } size_t rows() const { return R; } size_t cols() const { return C; } public: // operations Matrix<R,C>& operator+= (const Matrix<R,C>&); }; template<const size_t R, const size_t C> Matrix<R,C>::Matrix() { for (size_t row=0; row<R; ++row) for (size_t col=0; col<C; ++col) m_data[row][col] = 0; } template<const size_t R, const size_t C> Matrix<R,C>::Matrix(const Matrix<R,C>& source) { for (size_t row=0; row<R; ++row) for (size_t col=0; col<C; ++col) m_data[row][col] = source.m_data[row][col]; } template<const size_t R, const size_t C> Matrix<R,C>::Matrix(Matrix<R,C>&& source) { for (size_t row=0; row<R; ++row) for (size_t col=0; col<C; ++col) m_data[row][col] = std::move (source.m_data[row][col]); } template<const size_t R, const size_t C> Matrix<R,C>& Matrix<R,C>::operator= (const Matrix<R,C>& source) { for (size_t row=0; row<R; ++row) for (size_t col=0; col<C; ++col) m_data[row][col] = source.m_data[row][col]; return *this; } template<const size_t R, const size_t C> Matrix<R,C>& Matrix<R,C>::operator= (Matrix<R,C>&& source) { for (size_t row=0; row<R; ++row) for (size_t col=0; col<C; ++col) m_data[row][col] = std::move (source.m_data[row][col]); return *this; } template<const size_t R, const size_t C> Matrix<R,C>& Matrix<R,C>::operator+= (const Matrix<R,C>& rhs) { for (size_t row=0; row<R; ++row) for (size_t col=0; col<C; ++col) m_data[row][col] += rhs.m_data[row][col]; return *this; } template<const size_t R, const size_t C> Matrix<R,C> operator+ (const Matrix<R,C>& lhs, const Matrix<R,C>& rhs) { Matrix<R,C> sum (lhs); return sum += rhs; } template<const size_t R, const size_t C> std::ostream& operator<< (std::ostream& os, const Matrix<R,C>& m) { for (size_t row=0; row<R; ++row) { for (size_t col=0; col<C; ++col) { std::cout << m[row][col] << '\t'; } std::cout << std::endl; } return os; } int main() { srand ((unsigned)time(nullptr)); const size_t rows = 3; const size_t cols = 3; Matrix<rows, cols> a, b, c; for (size_t row=0; row<rows; ++row) { for (size_t col=0; col<cols; ++col) { a[row][col] = rand() % 10; b[row][col] = rand() % 10; } } std::cout << "Matrix a:\n\n" << a << '\n' << std::endl; std::cout << "Matrix b:\n\n" << b << '\n' << std::endl; std::cout << "Matrix a + b:\n\n" << a + b << '\n' << std::endl; }
Show that for a square matrix the linear dependence of the row vectors implies that of the column vectors and conversely.?
show that SQUARE MATRIX THE LINEAR DEPENDENCE OF THE ROW VECTOR?
Perform addition multiplication subtraction of 2-D array using Operator Overloading in C plus plus?
#include<iostream> #include<vector> #include<random> template<const size_t R, const size_t C> class Matrix { public: using row_type = int[C]; private: // attributes int m_data[R][C]; public: // construction/assignment Matrix (); Matrix (const Matrix& source); Matrix (Matrix&& source); Matrix& operator= (const Matrix<R,C>& source); Matrix& operator= (Matrix<R,C>&& source); ~Matrix () {} public: // accessors row_type& row (const size_t index) { return m_data[index]; } const row_type& row (const size_t index) const { return m_data[index]; } row_type& operator[] (const size_t index) { return m_data[index]; } const row_type& operator[] (const size_t index) const { return m_data[index]; } size_t size() const { return R * C; } size_t rows() const { return R; } size_t cols() const { return C; } public: // operations Matrix<R,C>& operator+= (const Matrix<R,C>&); Matrix<R,C>& operator-= (const Matrix<R,C>&); }; template<const size_t R, const size_t C> Matrix<R,C>::Matrix() { for (size_t row=0; row<R; ++row) for (size_t col=0; col<C; ++col) m_data[row][col] = 0; } template<const size_t R, const size_t C> Matrix<R,C>::Matrix(const Matrix<R,C>& source) { for (size_t row=0; row<R; ++row) for (size_t col=0; col<C; ++col) m_data[row][col] = source.m_data[row][col]; } template<const size_t R, const size_t C> Matrix<R,C>::Matrix(Matrix<R,C>&& source) { for (size_t row=0; row<R; ++row) for (size_t col=0; col<C; ++col) m_data[row][col] = std::move (source.m_data[row][col]); } template<const size_t R, const size_t C> Matrix<R,C>& Matrix<R,C>::operator= (const Matrix<R,C>& source) { for (size_t row=0; row<R; ++row) for (size_t col=0; col<C; ++col) m_data[row][col] = source.m_data[row][col]; return *this; } template<const size_t R, const size_t C> Matrix<R,C>& Matrix<R,C>::operator= (Matrix<R,C>&& source) { for (size_t row=0; row<R; ++row) for (size_t col=0; col<C; ++col) m_data[row][col] = std::move (source.m_data[row][col]); return *this; } template<const size_t R, const size_t C> Matrix<R,C>& Matrix<R,C>::operator+= (const Matrix<R,C>& rhs) { for (size_t row=0; row<R; ++row) for (size_t col=0; col<C; ++col) m_data[row][col] += rhs.m_data[row][col]; return *this; } template<const size_t R, const size_t C> Matrix<R,C>& Matrix<R,C>::operator-= (const Matrix<R,C>& rhs) { for (size_t row=0; row<R; ++row) for (size_t col=0; col<C; ++col) m_data[row][col] -= rhs.m_data[row][col]; return *this; } template<const size_t R, const size_t C> Matrix<R,C> operator+ (const Matrix<R,C>& lhs, const Matrix<R,C>& rhs) { Matrix<R,C> sum (lhs); return sum += rhs; } template<const size_t R, const size_t C> Matrix<R,C> operator- (const Matrix<R,C>& lhs, const Matrix<R,C>& rhs) { Matrix<R,C> sub (lhs); return sub -= rhs; } template<const size_t R, const size_t C, const size_t R1, const size_t C1> Matrix<R,C1> operator* (const Matrix<R,C>& lhs, const Matrix<R1,C1>& rhs) { static_assert (C==R1, "Matrix dimension mismatch!"); Matrix<R,C1> mul; for (size_t x=0; x!=R; ++x) { for (size_t y=0; y!=C1; ++y) { int prod = 0; for (size_t z=0; z!=C; ++z) { prod += lhs[x][z] * rhs[z][y]; } mul[x][y] = prod; } } return mul; } template<const size_t R, const size_t C> std::ostream& operator<< (std::ostream& os, const Matrix<R,C>& m) { for (size_t row=0; row<R; ++row) { for (size_t col=0; col<C; ++col) { std::cout << m[row][col] << '\t'; } std::cout << std::endl; } return os; } int main() { std::default_random_engine generator; std::uniform_int_distribution<int> distribution (1,9); const size_t rows = 2; const size_t cols = 3; Matrix<rows, cols> a, b; for (size_t row=0; row<rows; ++row) { for (size_t col=0; col<cols; ++col) { a[row][col] = distribution (generator); b[row][col] = distribution (generator); } } std::cout << "Matrix a:\n\n" << a << '\n' << std::endl; std::cout << "Matrix b:\n\n" << b << '\n' << std::endl; std::cout << "Matrix a + b:\n\n" << a + b << '\n' << std::endl; std::cout << "Matrix a - b:\n\n" << a - b << '\n' << std::endl; Matrix<cols, rows> c; for (size_t row=0; row<rows; ++row) { for (size_t col=0; col<cols; ++col) { c[col][row] = distribution (generator); } } std::cout << "Matrix c:\n\n" << c << '\n' << std::endl; std::cout << "Matrix a * c:\n\n" << a * c << '\n' << std::endl; }
What is a 1x2 matrix?
It is a matrix with 1 row and two columns: something like (x, y).
What is element a13 in this matrix?
To determine element a13 in a matrix, you need to identify its position based on the matrix's row and column indexing. In a typical matrix notation, a13 refers to the element located in the 1st row and 3rd column. If you provide the specific matrix, I can help you find the value of a13.
Does doing row operations on a matrix change its determinant?
No.
