Multiply the Matrices

Problem

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

Solution

1. Identify the dimensions of the matrices. Both are 3×3 matrices, so the resulting matrix will also be 3×3

2. Calculate the elements of the first row by multiplying the first row of the left matrix by each column of the right matrix.

(R_1)*(C_1)=(1)*(2)+(1)*(−1)+(2)*(−1)=2−1−2=−1

(R_1)*(C_2)=(1)*(−3)+(1)*(2)+(2)*(2)=−3+2+4=3

(R_1)*(C_3)=(1)*(0)+(1)*(1)+(2)*(0)=0+1+0=1

3. Calculate the elements of the second row by multiplying the second row of the left matrix by each column of the right matrix.

(R_2)*(C_1)=(1)*(2)+(−1)*(−1)+(1)*(−1)=2+1−1=2

(R_2)*(C_2)=(1)*(−3)+(−1)*(2)+(1)*(2)=−3−2+2=−3

(R_2)*(C_3)=(1)*(0)+(−1)*(1)+(1)*(0)=0−1+0=−1

4. Calculate the elements of the third row by multiplying the third row of the left matrix by each column of the right matrix.

(R_3)*(C_1)=(1)*(2)+(−1)*(−1)+(2)*(−1)=2+1−2=1

(R_3)*(C_2)=(1)*(−3)+(−1)*(2)+(2)*(2)=−3−2+4=−1

(R_3)*(C_3)=(1)*(0)+(−1)*(1)+(2)*(0)=0−1+0=−1

5. Assemble the calculated values into the resulting matrix.

Final Answer

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

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