Multiply the Matrices

Problem

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

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)=(4)*(6)+(0)*(1)+(0)*(3)=24

(R_1)*(C_2)=(4)*(0)+(0)*(5)+(0)*(2)=0

(R_1)*(C_3)=(4)*(0)+(0)*(0)+(0)*(6)=0

3. Calculate the elements of the second row.

(R_2)*(C_1)=(−2)*(6)+(0)*(1)+(0)*(3)=−12

(R_2)*(C_2)=(−2)*(0)+(0)*(5)+(0)*(2)=0

(R_2)*(C_3)=(−2)*(0)+(0)*(0)+(0)*(6)=0

4. Calculate the elements of the third row.

(R_3)*(C_1)=(−3)*(6)+(0)*(1)+(7)*(3)=−18+0+21=3

(R_3)*(C_2)=(−3)*(0)+(0)*(5)+(7)*(2)=0+0+14=14

(R_3)*(C_3)=(−3)*(0)+(0)*(0)+(7)*(6)=0+0+42=42

5. Assemble the resulting matrix using the calculated values.

Final Answer

[[4,0,0],[−2,0,0],[−3,0,7]]*[[6,0,0],[1,5,0],[3,2,6]]=[[24,0,0],[−12,0,0],[3,14,42]]

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