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Hit the second button, then '5'.
Hit '4' twice so the entry box reads "rref("
Enter your matrix in the form:
[[x1,x2,...,xn][y1,y2,...,yn][z1,z2,...,zn]]
Where each set of letters in a bracket coresponds to a rox of your matrix, for example:
| a b c |
| d e f |
| g h i |
would be entered as
"[[a,b,c][d,e,f][g,h,i]]"
Finally close the parenthesis and hit 'enter'.
What else can I help you with?
How to construct a matrix with 23 elements?
It will either be a 1*23 row matrix or a 23*1 column matrix.
How do you map multidimensional dense matrix to one dimensional matrix?
To map a multidimensional dense matrix to a one-dimensional matrix, you can use a linearization technique, which typically involves flattening the matrix. This can be achieved by iterating through each dimension in a specified order (e.g., row-major or column-major order) and appending the elements to a one-dimensional array. For example, in row-major order, you would traverse each row sequentially before moving to the next row. The resulting one-dimensional matrix will contain all the elements of the multidimensional matrix in the chosen order.
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.
Is every square matrix is a product of elementary matrices explain?
Yes, every square matrix can be expressed as a product of elementary matrices. This is because elementary matrices, which perform row operations, can be used to transform any square matrix into its row echelon form or reduced row echelon form through a series of row operations. Since any square matrix can be transformed into the identity matrix using these operations, it can be represented as a product of the corresponding elementary matrices that perform these transformations. Thus, every square matrix is indeed a product of elementary matrices.
What is row matrix?
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.
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; }
How do you solve 4 equation with 4 unknows?
Create a matrix of the coefficients of each equation. The solutions to the equations should make up the rightmost column of the matrix. Then, row reduce the matrix until you are able to rewrite the equations and solve them. The matrix should be a 4x5 matrix (4 rows and 5 columns) for four equations with four variables. This is known as a system of equations.
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?
How do you map multidimensional dense matrix to one dimensional matrix?
To map a multidimensional dense matrix to a one-dimensional matrix, you can use a linearization technique, which typically involves flattening the matrix. This can be achieved by iterating through each dimension in a specified order (e.g., row-major or column-major order) and appending the elements to a one-dimensional array. For example, in row-major order, you would traverse each row sequentially before moving to the next row. The resulting one-dimensional matrix will contain all the elements of the multidimensional matrix in the chosen order.
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; }
