Multiply the Matrices

Problem

[[5,−5,5],[−3,8,−1]]*[[9,−4,−7],[3,5,−1],[−1,3,−2]]

Solution

1. Identify the dimensions of the matrices. The first matrix is 2×3 and the second matrix is 3×3 so the resulting matrix will be 2×3

2. Calculate the first row, first column entry by taking the dot product of the first row of the first matrix and the first column of the second matrix.

(5)*(9)+(−5)*(3)+(5)*(−1)=45−15−5=25

3. Calculate the first row, second column entry.

(5)*(−4)+(−5)*(5)+(5)*(3)=−20−25+15=−30

4. Calculate the first row, third column entry.

(5)*(−7)+(−5)*(−1)+(5)*(−2)=−35+5−10=−40

5. Calculate the second row, first column entry.

(−3)*(9)+(8)*(3)+(−1)*(−1)=−27+24+1=−2

6. Calculate the second row, second column entry.

(−3)*(−4)+(8)*(5)+(−1)*(3)=12+40−3=49

7. Calculate the second row, third column entry.

(−3)*(−7)+(8)*(−1)+(−1)*(−2)=21−8+2=15

Final Answer

[[5,−5,5],[−3,8,−1]]*[[9,−4,−7],[3,5,−1],[−1,3,−2]]=[[25,−30,−40],[−2,49,15]]

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