Multiply the Matrices

Problem

[[0,1,0,0,0],[1,0,0,0,1],[0,0,0,1,1],[0,0,1,0,1],[0,1,1,1,0]]*[[0,1,0,0,0],[1,0,0,0,1],[0,0,0,1,1],[0,0,1,0,1],[0,1,1,1,0]]

Solution

1. Identify the dimensions of the matrices. Both are 5×5 matrices, so the resulting product will also be a 5×5 matrix.

2. Apply the dot product rule for each row of the first matrix and each column of the second matrix. The element at row i and column j is calculated as (c_i*j)=(∑_k=1^5)((a_i*k))*(b_k*j)

3. Calculate row 1:

   (c_11)=(0)*(0)+(1)*(1)+(0)*(0)+(0)*(0)+(0)*(0)=1

   (c_12)=(0)*(1)+(1)*(0)+(0)*(0)+(0)*(0)+(0)*(1)=0

   (c_13)=(0)*(0)+(1)*(0)+(0)*(0)+(0)*(1)+(0)*(1)=0

   (c_14)=(0)*(0)+(1)*(0)+(0)*(1)+(0)*(0)+(0)*(1)=0

   (c_15)=(0)*(0)+(1)*(1)+(0)*(1)+(0)*(1)+(0)*(0)=1

4. Calculate row 2:

   (c_21)=(1)*(0)+(0)*(1)+(0)*(0)+(0)*(0)+(1)*(0)=0

   (c_22)=(1)*(1)+(0)*(0)+(0)*(0)+(0)*(0)+(1)*(1)=2

   (c_23)=(1)*(0)+(0)*(0)+(0)*(0)+(0)*(1)+(1)*(1)=1

   (c_24)=(1)*(0)+(0)*(0)+(0)*(1)+(0)*(0)+(1)*(1)=1

   (c_25)=(1)*(0)+(0)*(1)+(0)*(1)+(0)*(1)+(1)*(0)=0

5. Calculate row 3:

   (c_31)=(0)*(0)+(0)*(1)+(0)*(0)+(1)*(0)+(1)*(0)=0

   (c_32)=(0)*(1)+(0)*(0)+(0)*(0)+(1)*(0)+(1)*(1)=1

   (c_33)=(0)*(0)+(0)*(0)+(0)*(0)+(1)*(1)+(1)*(1)=2

   (c_34)=(0)*(0)+(0)*(0)+(0)*(1)+(1)*(0)+(1)*(1)=1

   (c_35)=(0)*(0)+(0)*(1)+(0)*(1)+(1)*(1)+(1)*(0)=1

6. Calculate row 4:

   (c_41)=(0)*(0)+(0)*(1)+(1)*(0)+(0)*(0)+(1)*(0)=0

   (c_42)=(0)*(1)+(0)*(0)+(1)*(0)+(0)*(0)+(1)*(1)=1

   (c_43)=(0)*(0)+(0)*(0)+(1)*(0)+(0)*(1)+(1)*(1)=1

   (c_44)=(0)*(0)+(0)*(0)+(1)*(1)+(0)*(0)+(1)*(1)=2

   (c_45)=(0)*(0)+(0)*(1)+(1)*(1)+(0)*(1)+(1)*(0)=1

7. Calculate row 5:

   (c_51)=(0)*(0)+(1)*(1)+(1)*(0)+(1)*(0)+(0)*(0)=1

   (c_52)=(0)*(1)+(1)*(0)+(1)*(0)+(1)*(0)+(0)*(1)=0

   (c_53)=(0)*(0)+(1)*(0)+(1)*(0)+(1)*(1)+(0)*(1)=1

   (c_54)=(0)*(0)+(1)*(0)+(1)*(1)+(1)*(0)+(0)*(1)=1

   (c_55)=(0)*(0)+(1)*(1)+(1)*(1)+(1)*(1)+(0)*(0)=3

Final Answer

[[0,1,0,0,0],[1,0,0,0,1],[0,0,0,1,1],[0,0,1,0,1],[0,1,1,1,0]]*[[0,1,0,0,0],[1,0,0,0,1],[0,0,0,1,1],[0,0,1,0,1],[0,1,1,1,0]]=[[1,0,0,0,1],[0,2,1,1,0],[0,1,2,1,1],[0,1,1,2,1],[1,0,1,1,3]]

Want more problems? Check here!