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write a program to Implement addition , subtraction , transpose and multiplication in a matrix

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 Ques . write a program to Implement addition , subtraction , transpose and multiplication in a matrix

Answer :

 matrix is referred as  a  arrangement of numbers in rows and columns in which each number or a element is called matrix element .

Dimension of matrix : No. of rows X No. of columns . 

Example : [2,3]

                    [1,2]

therefore , dimension = 2 X 2 = 2 rows and 2 columns . 

Algorithm to add two matrices

  • Input  matrix X and matrix Y.
  • If the number of rows and number of columns of matrix X  and matrix Y is equal,
  1. for i =1 to rows [matrix X]  
  2. for j =1 to columns [matrix X]  
  • Input matrix X [i,j]
  • Input matrix Y [i,j]
  • matrix Result [i, j] = matrix X [i, j] + matrix Y [i, j];  

    3. Display matrix Result [i,j]

 Example : 

 X=[1,2,3]                Y=[2,3,4]   

        [0,1,0]                     [4,4,4]

Result = [1+2,2+3,3+4] = [3,5,7]

                [0+4,1+4,0+4] = [4,5,4]    

Algorithm to subtract two matrices

  • Input  matrix X and matrix Y.
  • If the number of rows and number of columns of matrix X  and matrix Y is equal,
  1. for i =1 to rows [matrix X]  
  2. for j =1 to columns [matrix X]  
  • Input matrix X [i,j]
  • Input matrix Y [i,j]
  • matrix Result [i, j] = matrix X [i, j] - matrix Y [i, j];  

    3. Display matrix Result [i,j]

 Example : 

 X=[1,2,3]                Y=[2,3,4]   

       [0,1,0]                     [4,4,4]

Result = [1-2,2-3,3-4] = [-1,-1,-1]

                [0-4,1-4,0-4] = [-4,-3,-4]             

Algorithm to perform matrix multiplication

  1. Input the matrix X elements
  2. Input the matrix Y elements
  3. Repeat from i = 0 to the length of the first matrix
  4. Repeat from j = 0 to the length of the first element
  5. Repeat from k = 0 to the length of the second matrix
  6. Result[i][j] += matrix X[i][j] * matrix Y[i][j]
  7. Print matrix Result
  8. End   

Example : X =  [[10, 9] [8, 6]]

Y = [[1, 2], [3, 4]]

XY= [(10*1+9*3) , (10*2+9*4)] = [37, 56]

[(8*1+6*3) , (8*2+6*4) ] = [26, 40]

Example to transpose of matrix : 

1   2   3
4   5   6
7   8   9

output:

1   4   7
2   5   8

3   6   9

Column wise addition, subtraction, multiplication and transpose : 

X = [[1,2,3], 

    [2 ,5,6], 

    [7 ,8,9]]   

Y = [[9,8,7], 

    [6,5,4], 

    [3,2,1]]   

result = [[0,0,0], 

        [0,0,0], 

        [0,0,0]] 

#addition

for i in range(len(X)):    

    for j in range(len(X[0])): 

        result[i][j] = X[i][j] + Y[i][j]   

for r in result: 

    print(r) 


#subtraction

for i in range(len(X)):    

    for j in range(len(X[0])): 

        result[i][j] = X[i][j] - Y[i][j]   

for r in result: 

    print(r)


#multiplication

for i in range(len(X)): 

    for j in range(len(Y[0])): 

        for k in range(len(Y)): 

            result[i][j] += X[i][k] * Y[k][j]  

for r in result: 

    print(r)


#transpose

for i in range(len(X)):

   for j in range(len(X[0])):

       result[j][i] = X[i][j]

for r in result:

   print(r)

Output : 

[10, 10, 10]

[8, 10, 10]

[10, 10, 10]


[-8, -6, -4]

[-4, 0, 2]

[4, 6, 8]


[22, 18, 14] 

[62, 53, 42] 

[142, 120, 98]


[1, 2, 7]

[2, 5, 8]

[3, 6, 9]


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