Question

In python and comments your code :

Exercise 1

1.Write a function waiting for two matrices and returning their addition, −1 if it is not not possible.
2. Write a function associated with a matrix and a scalar and returning the produced matrix.
3. Write a function accompanying an n × m matrix and a vector n and returning the vector produced by each other, −1 if this is not possible.
4. Write a function accompanying two n × m and m × k matrices and returning the product matrix, −1 if this is not possible.
5.Write a function waiting for a vector (column or row) and returning its transpose.

Exercise 2

1.Write a function waiting for a 2 × 2 matrix and calculating its determinant.
2. Write a function waiting for a matrix A of size n × m and two integers i and j and rendering a matrix (n − 1) × (m − 1), copy the matrix A without row i and column j .
3. Write a determining function of a square matrix by expanding on a line.

Answer 1

1. Function for addition:

def addition(x,y):
    if len(x)!=len(y) or len(x[0])!=len(y[0]):
        return -1
    
    result = [[ 0 for i in range(len(x))] for j in range(len(x[0]))]

    #iterate through rows
    for i in range(len(x)):
        #iterate through columns
        for j in range(len(x[0]):
            result[i][j] = x[i][j]+y[i][j]

    return result

2. Function for Matrix multiplied with Scalar:

def scalarMultiply(x, scalar):
    #traversing through rows
    for i in range(len(x)):
        #traversing through columns
        for j in range(len(y)):
            #multiplying with scalar
            x[i][j]*=scalar

    return scalar

3. Function for multiplication of vector with matrix:

def matrixMultiplication(X,Y):
    result = [[0 for i in range(len(X))] for j in range(len(Y[0]))]
    # iterate through rows of X
    for i in range(len(X)):
        #iterate through columns of Y
        for j in range(len(Y[0])):
           #iterate through rows of Y
           for k in range(len(Y)):
               result[i][j] += X[i][k] * Y[k][j]


def vectorMatrix(x, vector):
    #checking if vector is a column vector
    if len(vector[0])==len(x):
        result = matrixMultiplication(vector,x)

    #checking if vector is a row vector
    elif len(x[0])==len(vector):
        result = matrixMultiplication(x,vector)

    #The matrix and the vector can't be multiplied
    else
        result = -1
    
    return result
        

4. Function for Matrix Multiplication:

def matrixMultiplication(X,Y):
    #Matrices cannot be multiplied
    if len(X[0])!=len(Y):
        return -1

    result = [[0 for i in range(len(X))] for j in range(len(Y[0]))]
    # iterate through rows of X
    for i in range(len(X)):
        #iterate through columns of Y
        for j in range(len(Y[0])):
           #iterate through rows of Y
           for k in range(len(Y)):
               result[i][j] += X[i][k] * Y[k][j]

    return result

5. Function for transpose of a vector:

def transposeVector(vector):
    result = [[0 for i in range(vector)] for j in range(vector[0])]
    #iterate through rows
    for i in range(len(vector)):
        #iterate through columns
        for j in range(len(vector[0])):
            result[j][i] = vector[i][j]

    return result