Multiply the Matrices

Problem

[[0,0,0,0],[0,0,0,0],[−1,1,0,0],[2,2,0,0]]*[[0,0,−1,1],[0,0,1,1],[1,0,0,0],[0,1,0,0]]

Solution

1. Identify the dimensions of the matrices. Both are 4×4 matrices, so the resulting matrix will also be 4×4

2. Calculate the first two rows. Since the first two rows of the left matrix consist entirely of zeros, every element in the first two rows of the product will be zero.

(R_1)=[[0,0,0,0]]

(R_2)=[[0,0,0,0]]

3. Compute the third row by multiplying the third row of the left matrix by each column of the right matrix.

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

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

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

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

4. Compute the fourth row by multiplying the fourth row of the left matrix by each column of the right matrix.

(c_41)=(2)*(0)+(2)*(0)+(0)*(1)+(0)*(0)=0

(c_42)=(2)*(0)+(2)*(0)+(0)*(0)+(0)*(1)=0

(c_43)=(2)*(−1)+(2)*(1)+(0)*(0)+(0)*(0)=0

(c_44)=(2)*(1)+(2)*(1)+(0)*(0)+(0)*(0)=4

5. Assemble the resulting matrix using the calculated values.

Final Answer

[[0,0,0,0],[0,0,0,0],[−1,1,0,0],[2,2,0,0]]*[[0,0,−1,1],[0,0,1,1],[1,0,0,0],[0,1,0,0]]=[[0,0,0,0],[0,0,0,0],[0,0,2,0],[0,0,0,4]]

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