Multiply the Matrices

Problem

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

Solution

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

2. Calculate the elements of the first row.

(c_11)=(−1)*(2)+(1)*(0)+(1)*(1)=−2+0+1=−1

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

(c_13)=(−1)*(2)+(1)*(1)+(1)*(1)=−2+1+1=0

3. Calculate the elements of the second row.

(c_21)=(1)*(2)+(0)*(0)+(−2)*(1)=2+0−2=0

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

(c_23)=(1)*(2)+(0)*(1)+(−2)*(1)=2+0−2=0

4. Calculate the elements of the third row.

(c_31)=(−1)*(2)+(2)*(0)+(2)*(1)=−2+0+2=0

(c_32)=(−1)*(0)+(2)*(−1)+(2)*(1)=0−2+2=0

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

5. Assemble the resulting matrix using the calculated values.

Final Answer

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

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