The determinant of a matrix can be used to find if it is invertible or not. The matrix is invertible if the determinant is non-zero. So if the determinant comes out to be zero, the matrix is not invertible. For example −The given matrix is: 4 2 1 2 1 1 9 3 2 The determinant of the above matrix is: 3 So the matrix is invertible.A program that checks if a matrix is invertible or not is as follows.Example Live Demo#include #include using namespace std; int determinant( int matrix[10][10], int n) {    int det = 0;    int ... Read More

A matrix is a rectangular array of numbers that is arranged in the form of rows and columns.An example of a matrix is as follows.A 3*4 matrix has 3 rows and 4 columns as shown below.8 6 3 5 7 1 9 2 5 1 9 8A program that multiplies two matrices by passing the matrices to functions is as follows.Example Live Demo#include using namespace std; void MatrixMultiplication(int a[2][3],int b[3][3]) {    int product[10][10], r1=2, c1=3, r2=3, c2=3, i, j, k;    if (c1 != r2) {       cout

A structure is a collection of items of different data types. It is very useful in creating complex data structures with different data type records. A structure is defined with the struct keyword.An example of a structure is as follows −struct employee {    int empID;    char name[50];    float salary; };A program that stores and displays information using structure is given as follows.Example Live Demo#include using namespace std; struct employee {    int empID;    char name[50];    int salary;    char department[50]; }; int main() {    struct employee emp[3] = { { 1 , "Harry" , 20000 , "Finance" } , { 2 , "Sally" , 50000 , "HR" } ,    { 3 , "John" , 15000 , "Technical" } };    cout

Standard deviation is the measure of how spread out the numbers in the data are. It is the square root of variance, where variance is the average of squared differences from the mean.A program to calculate the standard deviation is given as follows.Example Live Demo#include #include using namespace std; int main() {    float val[5] = {12.5, 7.0, 10.0, 7.8, 15.5};    float sum = 0.0, mean, variance = 0.0, stdDeviation;    int i;    for(i = 0; i < 5; ++i)    sum += val[i];    mean = sum/5;    for(i = 0; i < 5; ++i)    variance += pow(val[i] - mean, 2);    variance=variance/5;    stdDeviation = sqrt(variance);    cout

A sparse matrix is a matrix in which majority of the elements are 0. In other words, if more than half of the elements in the matrix are 0, it is known as a sparse matrix. For example −The matrix given below contains 5 zeroes. Since the number of zeroes is more than half the elements of the matrix, it is a sparse matrix.1 0 2 5 0 0 0 0 9A program to check if it is a sparse matrix or not is as follows.Example Live Demo#include using namespace std; int main () {    int a[10][10] = { {2, ... Read More

A matrix is a rectangular array of numbers that is arranged in the form of rows and columns.An example of a matrix is as follows.A 3*2 matrix has 3 rows and 2 columns as shown below −8 1 4 9 5 6A program that performs matrix multiplication is as follows.Example Live Demo#include using namespace std; int main() {    int product[10][10], r1=3, c1=3, r2=3, c2=3, i, j, k;    int a[3][3] = { {2, 4, 1} , {2, 3, 9} , {3, 1, 8} };    int b[3][3] = { {1, 2, 3} , {3, 6, 1} , {2, 4, 7} };    if (c1 != r2) {       cout

Factorial of a non-negative integer n is the product of all the positive integers that are less than or equal to n.For example: The factorial of 4 is 24.4! = 4 * 3 * 2 *1 4! = 24The factorial of an integer can be found using a recursive program or an iterative program.The following program demonstrates a recursive program to find the factorial of a number −Example Live Demo#include using namespace std; int fact(int n) {    if ((n==0)||(n==1))    return 1;    else    return n*fact(n-1); } int main() {    int n = 4;    cout

Factorial of a non-negative integer n is the product of all the positive integers that are less than or equal to n.For example: The factorial of 6 is 720.6! = 6 * 5 * 4 * 3 * 2 *1 6! = 720The factorial of an integer can be found using a recursive program or an iterative program.A for loop can be used to find the factorial of a number using an iterative program. This is demonstrated as follows.Example Live Demo#include using namespace std; int main() {    int n = 6, fact = 1, i;    for(i=1; i

A string is a one-dimensional character array that is terminated by a null character. Frequency of characters in a string is the number of times they occur in a string. For example −String: Football is a sport The frequency of alphabet o in the above string is 3A program to find the frequency of a particular alphabet is given as follows.Example Live Demo#include using namespace std; int main() {    char str[100] = "this string contains many alphabets";    char c = 'a';    int count = 0;    for(int i = 0; str[i] != '\0'; i++) {       if(str[i] == c)       count++;    }    cout

In a computer system, the octal number is expressed in the octal numeral system while the decimal number is in the decimal numeral system. The octal number is in base 8 while the decimal number is in base 10.Examples of decimal numbers and their corresponding octal numbers are as follows.Decimal NumberOctal Number81070106253177A program that converts the decimal numbers into octal is as follows.Example Live Demo#include using namespace std; void DecimalToOctal(int decimalNum) {    int octalNum = 0, placeValue = 1;    int dNo = decimalNum;    while (decimalNum != 0) {       octalNum += (decimalNum % 8) * placeValue;       decimalNum /= 8;       placeValue *= 10;    }    cout