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What is the transpose of a matrix?
Take each row and convert it into a column. The first row becomes the first column, the second row, the second column, etc.
How to construct a matrix with 23 elements?
It will either be a 1*23 row matrix or a 23*1 column matrix.
What is an intersection of column and row?
A cell in a matrix (or 2-dimensional array).
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?
Write c plus plus program to find product of matrices?
#include<iostream> #include<iomanip> #include<vector> class matrix { private: // a vector of vectors std::vector< std::vector< int >> m_vect; public: // default constructor matrix(unsigned rows, unsigned columns) { // rows and columns must be non-zero if (!rows !columns) { throw; } m_vect.resize (rows); for (unsigned row=0; row<rows; ++row) { m_vect[row].resize (columns); for (unsigned column=0; column<columns; ++column) { m_vect[row][column] = 0; } } } // copy constructor matrix(const matrix& copy) { m_vect.resize (copy.rows()); for (unsigned row=0; row<copy.rows(); ++row) { m_vect[row] = copy.m_vect[row]; } } // assignment operator (uses copy/swap paradigm) matrix operator= (const matrix copy) { // note that copy was passed by value and was therefore copy-constructed // so no need to test for self-references (which should be rare anyway) m_vect.clear(); m_vect.resize (copy.rows()); for (unsigned row=0; row<copy.m_vect.size(); ++row) m_vect[row] = copy.m_vect[row]; } // allows vector to be used just as you would a 2D array (const and non-const versions) const std::vector< int >& operator[] (unsigned row) const { return m_vect[row]; } std::vector< int >& operator[] (unsigned row) { return m_vect[row]; } // product operator overload matrix operator* (const matrix& rhs) const; // read-only accessors to return dimensions const unsigned rows() const { return m_vect.size(); } const unsigned columns() const { return m_vect[0].size(); } }; // implementation of product operator overload matrix matrix::operator* (const matrix& rhs) const { // ensure columns and rows match if (columns() != rhs.rows()) { throw; } // instantiate matrix of required size matrix product (rows(), rhs.columns()); // calculate elements using dot product for (unsigned x=0; x<product.rows(); ++x) { for (unsigned y=0; y<product.columns(); ++y) { for (unsigned z=0; z<columns(); ++z) { product[x][y] += (*this)[x][z] * rhs[z][y]; } } } return product; } // output stream insertion operator overload std::ostream& operator<< (std::ostream& os, matrix& mx) { for (unsigned row=0; row<mx.rows(); ++row) { for (unsigned column=0; column<mx.columns(); ++column) { os << std::setw (10) << mx[row][column]; } os << std::endl; } return os; } int main() { matrix A(2,3); matrix B(3,4); int value=0, row, column; // initialise matrix A (incremental values) for (row=0; row<A.rows(); ++row) { for (column=0; column<A.columns(); ++column) { A[row][column] = ++value; } } std::cout << "Matrix A:\n\n" << A << std::endl; // initialise matrix B (incremental values) for (row=0; row<B.rows(); ++row) { for (column=0; column<B.columns(); ++column) { B[row][column] = ++value; } } std::cout << "Matrix B:\n\n" << B << std::endl; // calculate product of matrices matrix product = A * B; std::cout << "Product (A x B):\n\n" << product << std::endl; }
What is the minor of determinant?
The minor is the determinant of the matrix constructed by removing the row and column of a particular element. Thus, the minor of a34 is the determinant of the matrix which has all the same rows and columns, except for the 3rd row and 4th column.
Find a matrix A that is not invertible and b such that Ax equals b has a unique solution?
A matrix with a row or a column of zeros cannot have an inverse.Proof:Let A denote a matrix which has an entire row or column of zeros. If B is any matrix, then AB has an entire rows of zeros, or BA has an entire column of zeros. Thus, neither AB nor BA can be the identity matrix, so A cannot have an inverse, or A cannot be invertible.Since A is not invertible, then Ax = b has not a unique solution.
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 do You create a n by m matrix which contains 13 numbers?
It is either a row vector (1 x m matrix) or a column vector (n x 1 matrix).
What is a spreadsheet column?
It is apace provided for a set of data all occupying the same column in the spreadsheet's matrix so that they can be referenced as a set using the column header or individually by the column/row intersections.
Is the row space of matrix an equivalent to the column space of matrix AT which is the transpose of matrix A?
Since the columns of AT equal the rows of A by definition, they also span the same space, so yes, they are equivalent.
How to write incidence matrix?
An incidence matrix is a mathematical matrix showing a relationship between two different types of objects. The first class can be written as X and the second as Y with one row for each element of X and one column for each element of Y. The entry in row x and column 1 should be 1 if x and y are related to one another. The entry in row x and column 1 should be 0 if they are not related to each other,
