Multiply the Matrices

Problem

[[2,−1,3],[0,4,5],[−2,1,4]]*[[−18,−62,−33],[7,17,22],[11,−27,38]]

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

(R_1)*(C_1)=(2)*(−18)+(−1)*(7)+(3)*(11)=−36−7+33=−10

(R_1)*(C_2)=(2)*(−62)+(−1)*(17)+(3)*(−27)=−124−17−81=−222

(R_1)*(C_3)=(2)*(−33)+(−1)*(22)+(3)*(38)=−66−22+114=26

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

(R_2)*(C_1)=(0)*(−18)+(4)*(7)+(5)*(11)=0+28+55=83

(R_2)*(C_2)=(0)*(−62)+(4)*(17)+(5)*(−27)=0+68−135=−67

(R_2)*(C_3)=(0)*(−33)+(4)*(22)+(5)*(38)=0+88+190=278

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

(R_3)*(C_1)=(−2)*(−18)+(1)*(7)+(4)*(11)=36+7+44=87

(R_3)*(C_2)=(−2)*(−62)+(1)*(17)+(4)*(−27)=124+17−108=33

(R_3)*(C_3)=(−2)*(−33)+(1)*(22)+(4)*(38)=66+22+152=240

5. Assemble the resulting matrix using the calculated values.

Final Answer

[[2,−1,3],[0,4,5],[−2,1,4]]*[[−18,−62,−33],[7,17,22],[11,−27,38]]=[[−10,−222,26],[83,−67,278],[87,33,240]]

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