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Multiply the Matrices

Problem

[[3,−2,1],[−2,2,−1],[1,−1,1]]*[[1,0],[1,1],[0,2]]

Solution

  1. Identify the dimensions of the matrices. The first matrix is 3×3 and the second is 3×2 so the resulting matrix will be 3×2

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

(c_11)=(3)*(1)+(−2)*(1)+(1)*(0)=3−2+0=1

(c_12)=(3)*(0)+(−2)*(1)+(1)*(2)=0−2+2=0

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

(c_21)=(−2)*(1)+(2)*(1)+(−1)*(0)=−2+2+0=0

(c_22)=(−2)*(0)+(2)*(1)+(−1)*(2)=0+2−2=0

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

(c_31)=(1)*(1)+(−1)*(1)+(1)*(0)=1−1+0=0

(c_32)=(1)*(0)+(−1)*(1)+(1)*(2)=0−1+2=1

  1. Assemble the resulting values into the final 3×2 matrix.

Final Answer

[[3,−2,1],[−2,2,−1],[1,−1,1]]*[[1,0],[1,1],[0,2]]=[[1,0],[0,0],[0,1]]

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