Multiply the Matrices

Problem

[[0,6095,−6095],[6095,−6095,6095],[−6095,−6095,6095]]*[[20,3,18],[24,6,24],[14,12,20]]

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 first row of the product by multiplying the first row of the left matrix by each column of the right matrix.

(R_1)*(C_1)=(0)*(20)+(6095)*(24)+(−6095)*(14)=146280−85330=60950

(R_1)*(C_2)=(0)*(3)+(6095)*(6)+(−6095)*(12)=36570−73140=−36570

(R_1)*(C_3)=(0)*(18)+(6095)*(24)+(−6095)*(20)=146280−121900=24380

3. Calculate the second row of the product by multiplying the second row of the left matrix by each column of the right matrix.

(R_2)*(C_1)=(6095)*(20)+(−6095)*(24)+(6095)*(14)=121900−146280+85330=60950

(R_2)*(C_2)=(6095)*(3)+(−6095)*(6)+(6095)*(12)=18285−36570+73140=54855

(R_2)*(C_3)=(6095)*(18)+(−6095)*(24)+(6095)*(20)=109710−146280+121900=85330

4. Calculate the third row of the product by multiplying the third row of the left matrix by each column of the right matrix.

(R_3)*(C_1)=(−6095)*(20)+(−6095)*(24)+(6095)*(14)=−121900−146280+85330=−182850

(R_3)*(C_2)=(−6095)*(3)+(−6095)*(6)+(6095)*(12)=−18285−36570+73140=18285

(R_3)*(C_3)=(−6095)*(18)+(−6095)*(24)+(6095)*(20)=−109710−146280+121900=−134090

Final Answer

[[0,6095,−6095],[6095,−6095,6095],[−6095,−6095,6095]]*[[20,3,18],[24,6,24],[14,12,20]]=[[60950,−36570,24380],[60950,54855,85330],[−182850,18285,−134090]]

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