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Multiply Two Matrices

Certification: Basic Level Accuracy: 66.67% Submissions: 3 Points: 8

Write a C# program to multiply two matrices. Given two matrices A of dimension m×n and B of dimension n×p, calculate their product C of dimension m×p. The matrix multiplication rule states that C[i,j] = sum(A[i,k] * B[k,j]) for k from 0 to n-1.

Example 1
    
        
  • Input: 
            Matrix A = [
    
  [1, 2],
    
  [3, 4]
]

    Matrix B = [
    
  [5, 6],
    
  [7, 8]
]
    • 
        
  • Output: [
    
  [19, 22],
    
  [43, 50]
]
    • 
        
  • Explanation:
            
      
                
    • Step 1: Verify matrices can be multiplied by checking if the number of columns in A equals the number of rows in B.
      • 
                
    • Step 2: Create a result matrix C with dimensions m×p (rows of A × columns of B).
      • 
                
    • Step 3: For each element C[i,j], calculate the sum of products A[i,k] * B[k,j] for all valid k values (0 to n-1).
      • 
                
    • Step 4: Calculate each element:
                    
        
                        
      • C[0,0] = A[0,0]*B[0,0] + A[0,1]*B[1,0] = 1*5 + 2*7 = 5 + 14 = 19
        • 
                        
      • C[0,1] = A[0,0]*B[0,1] + A[0,1]*B[1,1] = 1*6 + 2*8 = 6 + 16 = 22
        • 
                        
      • C[1,0] = A[1,0]*B[0,0] + A[1,1]*B[1,0] = 3*5 + 4*7 = 15 + 28 = 43
        • 
                        
      • C[1,1] = A[1,0]*B[0,1] + A[1,1]*B[1,1] = 3*6 + 4*8 = 18 + 32 = 50
        • 
                    
      
                
      • 
            
    
        
    •
Example 2
    
        
  • Input:
            Matrix A = [
    
  [1, 2, 3],
    
  [4, 5, 6]
]

    Matrix B = [
    
  [7, 8],
    
  [9, 10],
    
  [11, 12]
]
    • 
        
  • Output: [
    
  [58, 64],
    
  [139, 154]
]
    • 
        
  • Explanation:
            
      
                
    • Step 1: Verify matrices can be multiplied by checking if the number of columns in A equals the number of rows in B.
      • 
                
    • Step 2: Create a result matrix C with dimensions m×p (rows of A × columns of B).
      • 
                
    • Step 3: For each element C[i,j], calculate the sum of products A[i,k] * B[k,j] for all valid k values (0 to n-1).
      • 
                
    • Step 4: Calculate each element:
                    
        
                        
      • C[0,0] = 1*7 + 2*9 + 3*11 = 7 + 18 + 33 = 58
        • 
                        
      • C[0,1] = 1*8 + 2*10 + 3*12 = 8 + 20 + 36 = 64
        • 
                        
      • C[1,0] = 4*7 + 5*9 + 6*11 = 28 + 45 + 66 = 139
        • 
                        
      • C[1,1] = 4*8 + 5*10 + 6*12 = 32 + 50 + 72 = 154
        • 
                    
      
                
      • 
            
    
        
    •
Constraints
    
        
  • 1 ≤ A.rows, A.columns, B.rows, B.columns ≤ 100
    • 
        
  • A.columns == B.rows (required for matrix multiplication)
    • 
        
  • -1000 ≤ A[i][j], B[i][j] ≤ 1000
    • 
        
  • Time Complexity: O(m*n*p)
    • 
        
  • Space Complexity: O(m*p)
    •
ArraysNumberTech MahindraPwC
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Hint
Solution

Solution Hints

    
        
  • Verify that the number of columns in matrix A equals the number of rows in matrix B.
    • 
        
  • Create a result matrix of size m×p.
    • 
        
  • Use three nested loops: one for rows in A, one for columns in B, and one for the common dimension.
    • 
        
  • Calculate each element of the result matrix using the formula C[i,j] = sum(A[i,k] * B[k,j]) for all k.
    • 
        
  • Optimize inner loops for better cache performance if necessary.
    •

Steps to solve by this approach:

 Step 1: Verify matrices can be multiplied by checking if the number of columns in A equals the number of rows in B.
 Step 2: Create a result matrix C with dimensions m×p (rows of A × columns of B).
 Step 3: Use three nested loops - one iterating through rows of A, one through columns of B, and one through the common dimension.
 Step 4: For each element C[i,j], calculate the sum of products A[i,k] * B[k,j] for all valid k values.
 Step 5: Return the resulting product matrix C.

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