Multiply the Matrices

Problem

[[−1,−2/5,1],[−4,1,1],[1,0,0]]*[[2,2,8],[5,−1,−7],[0,0,2]]

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.

(R_1)*(C_1)=(−1)*(2)+(−2/5)*(5)+(1)*(0)=−2−2+0=−4

(R_1)*(C_2)=(−1)*(2)+(−2/5)*(−1)+(1)*(0)=−2+2/5+0=−8/5

(R_1)*(C_3)=(−1)*(8)+(−2/5)*(−7)+(1)*(2)=−8+14/5+2=−6+14/5=−16/5

3. Calculate the elements of the second row.

(R_2)*(C_1)=(−4)*(2)+(1)*(5)+(1)*(0)=−8+5+0=−3

(R_2)*(C_2)=(−4)*(2)+(1)*(−1)+(1)*(0)=−8−1+0=−9

(R_2)*(C_3)=(−4)*(8)+(1)*(−7)+(1)*(2)=−32−7+2=−37

4. Calculate the elements of the third row.

(R_3)*(C_1)=(1)*(2)+(0)*(5)+(0)*(0)=2

(R_3)*(C_2)=(1)*(2)+(0)*(−1)+(0)*(0)=2

(R_3)*(C_3)=(1)*(8)+(0)*(−7)+(0)*(2)=8

5. Assemble the resulting matrix using the calculated values.

Final Answer

[[−1,−2/5,1],[−4,1,1],[1,0,0]]*[[2,2,8],[5,−1,−7],[0,0,2]]=[[−4,−8/5,−16/5],[−3,−9,−37],[2,2,8]]

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