Multiply the Matrices

Problem

[[−3,2,10,−9],[3,5,−8,−6]]*[[10,5],[−3,8],[2,3],[1,5]]

Solution

1. Identify the dimensions of the matrices. The first matrix is 2×4 and the second is 4×2 so the resulting matrix will be 2×2

2. Calculate the element in the first row, first column ((c_11) by taking the dot product of the first row of the first matrix and the first column of the second matrix.

(c_11)=(−3)*(10)+(2)*(−3)+(10)*(2)+(−9)*(1)=−30−6+20−9=−25

3. Calculate the element in the first row, second column ((c_12) by taking the dot product of the first row of the first matrix and the second column of the second matrix.

(c_12)=(−3)*(5)+(2)*(8)+(10)*(3)+(−9)*(5)=−15+16+30−45=−14

4. Calculate the element in the second row, first column ((c_21) by taking the dot product of the second row of the first matrix and the first column of the second matrix.

(c_21)=(3)*(10)+(5)*(−3)+(−8)*(2)+(−6)*(1)=30−15−16−6=−7

5. Calculate the element in the second row, second column ((c_22) by taking the dot product of the second row of the first matrix and the second column of the second matrix.

(c_22)=(3)*(5)+(5)*(8)+(−8)*(3)+(−6)*(5)=15+40−24−30=1

Final Answer

[[−3,2,10,−9],[3,5,−8,−6]]*[[10,5],[−3,8],[2,3],[1,5]]=[[−25,−14],[−7,1]]

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