Question

Question A matrix of dimensions m × n (an m-by-n matrix) is an ordered collection of m × n elements. which are called eernents (or components). The elements of an (m × n)-dimensional matrix A are denoted as a,, where 1im and1 S, symbolically, written as, A-a(1,1) S (i.j) S(m, ). Written in the familiar notation: 01,1 am Gm,n A3×3matrix The horizontal and vertical lines of entries in a matrix are called rows and columns, respectively A matrix with the same nmber of rows and columns is called a square matrix Several operations are defined for matrices, you are asked to implement the following: .Addition: the matrix addition is defined as ab Matrices A and B must have same dimensions. For examp le: 2 6 10 4 5 6| +12 5 8 =14+2 5+5 6+5 -16 10 14 10 14 18 1+1 2+4 3+ 3 6 9 7+3 8+6 9+9 Scaler multiplication Matrix A multiplied by scaler k is defined as kxa example: For 2. 4 5 6 8 10 12 14 16 18 as, wherei Trace The trace of a square matriz is the sum of its diagonal elements, namely j. For instance tr 4 5 61+5+9-15 anspose The transpose of a matrix is simply inverting the column and rows, namely a,,-01, Fr instance. 2 4 5 62 5 8 3 6 9 ·Matrix multiply Assume A is a m × k matrix and B is a k × n nnatrix, the product of AB is defined as You are asked to complete the implementation of a Python dass that can be used to represent matrices and perform various operations on them. The elements of a matrix are passed as a nested list to the constructor of the class, e.g., Matrix(E[1, 2, 3], [4, 5, 6], 17, 8, 9]]) creates an object representing the mat rix 1 2 3 4 5 6 7 89 In the code you impleent, make sure to check whether the matrices dimensions match so that the computation can be carried out. Pay attention to the bold italic font. In any case the operation is invalid (dimension mismatch, for instance), return an empty Matrix, namely with zero row and zero column. If the matrix passed to operator trace is not a square matrix, return float('inf) Note: you should write your own code for all the matrix operations. Do not import non-default python library like numpy. Follow the docstring provided to you, closely TODO: Download the file lab8.py, complete the functions inside according to their de- scriptions and upload your version of lab8.py to MarkUs. Feel free to add new helper func- tions/methods, but al the functions defined for you should be implemented. class Matrix(object) def __init__(self, matrix): '"(Matrix, list)- NoneType creates a data attribute elements and instantiate it to the matrix Preconditions: list e contains 2 sublists, all the sublists in e have the same length Complete the instance variable definitions DO NOT CHANGE THE VARIABLE NAMES. Feel free to add new ones self.elements matrix self.cols -... # number of columns self, rows # number of rows def __str__(self): ''"(Matrix) -> str returns a string representation of the elements of the matrix. When passed to print) this representation should result in the original matrix being displayed as fbllows: each row will be displayed on a separate line, with each element in a row separated from the next by one, and only one blank space. The string representation should not contain any additional blank spaces. Print nothing if the matrix is empty >>>print(MatrixCIC1,2], [3,4]])]) 1 2 >>> print(Matrix([[0,-1.5,2.0], [-1, 4.5, 0]])) 1 4.50 >>>print(MatrixCEDI)) pass def __repr_(self): """Do not change this.""" return self.--str def __eq_(self, other): '""(Matrix) -> bool Returns if the self matrix is equal Celementwise) to the other matrix >>>Matrix(E[1,1], 01,1]])Matrix(EC1,1], [1,1]]) True >>>Matrix(E[1,1], 01,2]])Matrix(EC1,1], [1,1]]) False pass def add(self, other): '""(Matrix, Matrix) -> Matrix Returns the result Cas a new Matrix object) of adding the second input Matrix to the first. Return an empty matrix if the matrices has mismatching sizes >>>Matrix(E[1,1], 01,1]]).add(Matrix(CL-1,3], [0,0]])) >>>MatrixCEC-1,3,0], [0,0,0], 01.5,1,1]]).add(Matrix(L[2,-0.5,1], [0,0,0], L0,0,11])) 1 2.5 1 1.5 1 2 pass def mul(self, k): "(Matrix, Matrix) -> Matrix Returns the scalar product of the input matrix with scalar k as a new matrix onject. >>>Matrix(E[1,1], 01,1]]).mul(1) >>>Matrix(E[1,3], [-2,-1]]).mulC-1) 2 1 pass def sub(self, other): '""(Matrix, Matrix) -> Matrix Returns the result Cas a new Matrix object) of subtract the second input Matrix to the first. Return an empty matrix if the matrices has mismatching sizes. >>>Matrix(E[1,1], 01,1]]).sub(Matrix(CL-1,3], [0,0]])) 2-2 >>>MatrixCEC-1,3,0], [0,0,0], 01.5,1,1]]).sub(Matrix(L[2,-0.5,1], [0,0,0], L0,0,11])) 3 3.5-1 1.5 1 0 pass def trace(self): (Matrix) -> float Returns the trace of the input matrix as a floating point number. If the matrix is not square, return float('inf MatrixCE01,1], 02,21]).traceC) MatrixCCC-1,3,0],o,0,0],[1.5,1,1]]).trace 3.0 0.0 pass def transpose(self): (Matrix) -> Matrix Returns the transpose of the input matrix as a new Matrix object. MatrixCEC1,2], [3,411).transposeC) 1 3 2 4 pass def dot(self, other): (Matrix, Matrix) -> Matrix Returns a matrix product between self and other. If self and other has mismatching dimension, return an empty Matrix object. If not, return the result of self (dot) other >AMatrixcEC1,2], [3,4], [5,6]]) >A.dot(A.transposeO) 11 25 39 17 39 61 pass

Answer 1

A): Programming code for Matrix Addition %%%%%% Using nested loop%%%%%%%

X = [[12,7,3], [4 ,5,6], [7 ,8,9]]

Y = [[5,8,1], [6,7,3], [4,5,9]]

result = [[0,0,0], [0,0,0], [0,0,0]]

%%%%% 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]

for r in result:
print(r)

Output:

[17, 15, 4]
[10, 12, 9]
[11, 13, 18]
B):Programming code for Matrix Scalar Multiplication

%%%% product of a matrix

%%%%%Size of given matrix

N = 3

def scalarProductMat( mat, k):

%%%%%scalar element is multiplied

%%%%% by the matrix

for i in range( N):

for j in range( N):

mat[i][j] = mat[i][j] * k   

%%%% Driver code

if _name_ == "__main__":

mat = [[ 1, 2, 3 ], [ 4, 5, 6 ], [ 7, 8, 9 ]]

k = 4

scalarProductMat(mat, k)

%%%% to display the resultant matrix

print("Scalar Product Matrix is : ")

for i in range(N):

for j in range(N):

print(mat[i][j], end = " ")

Output:

Scalar Product Matrix is :
4 8 12
16 20 24
28 32 36
C)Programming code for Matrix Trace:

import math

%%%% Size of given matrix

MAX = 100;

Returns trace of a matrix of

%%%% size n x n

def findTrace(mat, n):

sum = 0;

for i in range(n):

sum += mat[i][i];

return sum;

%%%%%Driver Code

mat = [[1, 1, 1, 1, 1],

[2, 2, 2, 2, 2],

[3, 3, 3, 3, 3],

[4, 4, 4, 4, 4],

[5, 5, 5, 5, 5]];

print("Trace of Matrix =", findTrace(mat, 5));

print("Normal of Matrix =", findNormal(mat, 5));

Output:

Trace of matrix = 15
D):Programming code for Matrix Transpose:

X = [[12,7], [4 ,5], [3 ,8]]

result = [[0,0,0], [0,0,0]]

%%%%% iterate through rows
for i in range(len(X)):
%%%%iterate through columns
for j in range(len(X[0])):
result[j][i] = X[i][j]

for r in result:
print(r)

Output:

[12, 4, 3]
[7, 5, 8]
E)Programming code forMatrix Multiplication:

%%%%% Matrix of order 3x3
X = [[12,7,3], [4 ,5,6], [7 ,8,9]]
%%%% Matrix of order 3x4
Y = [[5,8,1,2], [6,7,3,0], [4,5,9,1]]
%%%% Result is of order 3x4
result = [[0,0,0,0], [0,0,0,0], [0,0,0,0]]

%%%%%% 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]

for r in result:
print(r)

Output:

[114, 160, 60, 27]
[74, 97, 73, 14]
[119, 157, 112, 23]