Multiply the Matrices

Problem

2*[[−1,2,−1,1,−1,2],[−7,2,−7,0,−2,5],[3,3,−3,0,−1,7],[7,2,7,−3,0,−3],[3,−1,4,5,2,−4],[−2,−9,12,2,0,2]]*[[−6,−1,−3,−6,−1,9],[2,−1,4,3,−7,1],[0,2,−7,−9,6,−7],[−3,2,−6,−11,−6,0],[−7,−1,5,−5,13,−4],[1,−5,−9,6,−1,5]]

Solution

1. Multiply the two 6×6 matrices using the dot product of rows from the first matrix and columns from the second matrix.

2. Calculate the entry for row 1, column 1: (−1)*(−6)+(2)*(2)+(−1)*(0)+(1)*(−3)+(−1)*(−7)+(2)*(1)=6+4+0−3+7+2=16

3. Calculate all other entries of the product matrix C where (C_i*j)=(∑_k=1^6)((A_i*k))*(B_k*j)

4. Result of the matrix multiplication A×B

[[16,−11,1,−1,−30,14],[57,−31,27,151,−84,−1],[−1,−41,1,−10,−54,89],[−49,14,−41,−111,24,0],[−43,34,−37,−136,48,−25],[10,21,−144,−131,131,−101]]

5. Distribute the scalar factor of 2 to every entry in the resulting matrix.

Final Answer

2*[[−1,2,−1,1,−1,2],[−7,2,−7,0,−2,5],[3,3,−3,0,−1,7],[7,2,7,−3,0,−3],[3,−1,4,5,2,−4],[−2,−9,12,2,0,2]]*[[−6,−1,−3,−6,−1,9],[2,−1,4,3,−7,1],[0,2,−7,−9,6,−7],[−3,2,−6,−11,−6,0],[−7,−1,5,−5,13,−4],[1,−5,−9,6,−1,5]]=[[32,−22,2,−2,−60,28],[114,−62,54,302,−168,−2],[−2,−82,2,−20,−108,178],[−98,28,−82,−222,48,0],[−86,68,−74,−272,96,−50],[20,42,−288,−262,262,−202]]

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