Multiply the Matrices

Problem

[[−3,1,1],[−6,2,1],[−2,1,0]]*[[3,−7,−10],[10,−2,8],[5,4,−5]]

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)=(−3)*(3)+(1)*(10)+(1)*(5)=−9+10+5=6

(c_12)=(−3)*(−7)+(1)*(−2)+(1)*(4)=21−2+4=23

(c_13)=(−3)*(−10)+(1)*(8)+(1)*(−5)=30+8−5=33

3. Calculate the elements of the second row.

(c_21)=(−6)*(3)+(2)*(10)+(1)*(5)=−18+20+5=7

(c_22)=(−6)*(−7)+(2)*(−2)+(1)*(4)=42−4+4=42

(c_23)=(−6)*(−10)+(2)*(8)+(1)*(−5)=60+16−5=71

4. Calculate the elements of the third row.

(c_31)=(−2)*(3)+(1)*(10)+(0)*(5)=−6+10+0=4

(c_32)=(−2)*(−7)+(1)*(−2)+(0)*(4)=14−2+0=12

(c_33)=(−2)*(−10)+(1)*(8)+(0)*(−5)=20+8+0=28

5. Assemble the resulting matrix using the calculated values.

Final Answer

[[−3,1,1],[−6,2,1],[−2,1,0]]*[[3,−7,−10],[10,−2,8],[5,4,−5]]=[[6,23,33],[7,42,71],[4,12,28]]

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