Multiply the Matrices

Problem

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

Solution

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

2. Calculate the elements of the first row by taking the dot product of the first row of the left matrix with each column of the right matrix.

(R_1)*(C_1)=(2)*(2)+(1)*(4)+(3)*(2)=4+4+6=14

(R_1)*(C_2)=(2)*(1)+(1)*(2)+(3)*(6)=2+2+18=22

(R_1)*(C_3)=(2)*(3)+(1)*(7)+(3)*(10)=6+7+30=43

3. Calculate the elements of the second row by taking the dot product of the second row of the left matrix with each column of the right matrix.

(R_2)*(C_1)=(4)*(2)+(2)*(4)+(7)*(2)=8+8+14=30

(R_2)*(C_2)=(4)*(1)+(2)*(2)+(7)*(6)=4+4+42=50

(R_2)*(C_3)=(4)*(3)+(2)*(7)+(7)*(10)=12+14+70=96

4. Calculate the elements of the third row by taking the dot product of the third row of the left matrix with each column of the right matrix.

(R_3)*(C_1)=(1)*(2)+(3)*(4)+(5)*(2)=2+12+10=24

(R_3)*(C_2)=(1)*(1)+(3)*(2)+(5)*(6)=1+6+30=37

(R_3)*(C_3)=(1)*(3)+(3)*(7)+(5)*(10)=3+21+50=74

5. Assemble the resulting matrix using the calculated values.

Final Answer

[[2,1,3],[4,2,7],[1,3,5]]*[[2,1,3],[4,2,7],[2,6,10]]=[[14,22,43],[30,50,96],[24,37,74]]

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