Given a matrix M[r][c] with ‘r’ number of rows and ‘c’ number of columns, we have to check that the given matrix is Markov matrix or not. If the input matrix is Markov matrix then print the output “It is a Markov matrix” and “it’s not an Markov matrix” if it is not a Markov matrix.Markov MatrixNow, what is Markov Matrix? A matrix M is a Markov matrix if and only if its sum of each row is equal to only 1.Like in the given example below −$$\begin{bmatrix}0.2 & 0.3 & 0.5 \0.1 & 0.7 & 0.2 \0.4 & 0.5 ... Read More

Given a square matrix M[r][c] where ‘r’ is some number of rows and ‘c’ are columns such that r = c, we have to check that ‘M’ is upper triangular matrix or not.Upper Triangular MatrixUpper triangular matrix is a matrix in which the elements above the main diagonal(including the main diagonal) are not zero and below elements are zero only.Like in the given Example below −In above figure the red highlighted elements are lower elements from the main diagonal which are zero and rest elements are non-zero.ExampleInput: m[3][3] = { {1, 2, 3},    {0, 5, 6},    {0, 0, ... Read More

Given a square matrix M[r][c] where ‘r’ is some number of rows and ‘c’ are columns such that r = c, we have to check that ‘M’ is lower triangular matrix or not.Lower Triangular Matrix −Lower triangular matrix is a matrix in which the elements below the main diagonal(including the main diagonal) are not zero and above elements are zero only.Like in the given Example below −In above figure the red highlighted elements are upper elements from the main diagonal which are zero and rest elements are non-zero.ExampleInput: m[3][3] = { {1, 0, 0},    {2, 3, 0},    {4, ... Read More

Given a matrix M[r][c], ‘r’ denotes number of rows and ‘c’ denotes number of columns such that r = c forming a square matrix. We have to check whether the given square matrix is an Involutory matrix or not.Involutory MatrixA matrix is called Involutory matrix if and only if, when a matrix gets multiplied with itself and its result is an identity matrix. A matrix I is Identity matrix if and only if its main diagonal is one and other elements than the main diagonal are zero. So, we can say a matrix is Involutory matrix if and only if ... Read More

Given a matrix M[r][c], ‘r’ denotes number of rows and ‘c’ denotes number of columns such that r = c forming a square matrix. We have to check whether the given square matrix is an Idempotent matrix or not.Idempotent MatrixA matrix ‘M’ is called Idempotent matrix if and only the matrix ‘M’ multiplied by itself returns the same matrix ‘M’ i.e. M * M = M.Like in the given example below −We can say that the above matrix is multiplied by itself and returns the same matrix; hence the matrix is Idempotent matrix. ExampleInput: m[3][3] = { {2, -2, -4},   ... Read More

Given a matrix M[r][c], ‘r’ denotes number of rows and ‘c’ denotes number of columns such that r = c forming a square matrix. We have to find whether the given square matrix is diagonal and scalar matrix or not, if it is diagonal and scalar matrix then print yes in the result.Diagonal matrixA square matrix m[][] will be diagonal matrix if and only if the elements of the except the main diagonal are zero.Like in the given figure below −Here, the elements in the red are main diagonal which are non-zero rest elements except the main diagonal are zero making it a Diagonal ... Read More

Given with the length into centimeter as an input, the task is to convert the given length into meter and kilometreWe can use length conversion formula for this −1 m = 100 cm 1 km = 100000 cmExampleInput-: centimetre = 100 Output -: Length in meter = 3m    Length in Kilometer = 0.003kmAlgroithmStart Step 1 -> Declare variables as centimetre, meter, kilometre Step 2 -> set centimetre=100 Step 3 -> Set meter = centimeter / 100.0 Step 4 -> Set kilometer = centimeter / 100000.0 Step 5 -> print meter and kilometer StopExample#include using namespace std; int main(){    float centimeter, meter, kilometer;    centimeter = 300;    // Converting centimeter into meter and kilometer    meter = centimeter / 100.0;    kilometer = centimeter / 100000.0;    cout

Given with n C r, where C represents combination, n represents total numbers and r represents selection from the set, the task is to calculate the value of nCr.Combination is the selection of data from the given in a without the concern of arrangement. Permutation and combination differs in the sense that permutation is the process of arranging whereas combination is the process of selection of elements from the given set.Formula for permutation is -:nPr = (n!)/(r!*(n-r)!)ExampleInput-: n=12 r=4 Output-: value of 12c4 is :495AlgorithmStart Step 1 -> Declare function for calculating factorial    int cal_n(int n)    int temp ... Read More

Given with sides depending upon the type of base of pyramid the task is to calculate the volume of pyramid.Pyramid is a 3-D figure whose outer surfaces are triangular meeting at the common point forming the sharp edge of pyramid. Volume of pyramid depends upon the type of base it will have.There are different types of base a pyramid can be made up of, like −Triangular −It means pyramid will have triangular base, than the volume of pyramid will beFormula - : (1/6) * a * b * hSquare −It means pyramid will have square base, than the volume of ... Read More

Given with r1, r2 and r3 the task is to find the volume of ellipsoid. An ellipsoid is a quadric surface, a surface that may be defined as the zero set of a polynomial of degree two in three variables. Among quadric surfaces, an ellipsoid is characterized by either of the two following properties.Formula used to calculate volume of ellipsoidVolume of Ellipsoid : (4/3) * pi * r1 * r2 * r3ExampleInput-: r1 = 6.3, r2 = 43.4, r3 = 3.7 Output-: volume of ellipsoid is : 4224.87AlgorithmStart Step 1 -> define macro as    #define pi 3.14 Step 2 ... Read More