Multiply the Matrices

Problem

[[1,2,1],[0,1,2],[0,4,3]]*[[1,2,−3],[0,1,2],[−1,2,0]]

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

(c_11)=(1)*(1)+(2)*(0)+(1)*(−1)=0

(c_12)=(1)*(2)+(2)*(1)+(1)*(2)=6

(c_13)=(1)*(−3)+(2)*(2)+(1)*(0)=1

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

(c_21)=(0)*(1)+(1)*(0)+(2)*(−1)=−2

(c_22)=(0)*(2)+(1)*(1)+(2)*(2)=5

(c_23)=(0)*(−3)+(1)*(2)+(2)*(0)=2

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

(c_31)=(0)*(1)+(4)*(0)+(3)*(−1)=−3

(c_32)=(0)*(2)+(4)*(1)+(3)*(2)=10

(c_33)=(0)*(−3)+(4)*(2)+(3)*(0)=8

5. Assemble the calculated values into the final matrix format.

Final Answer

[[1,2,1],[0,1,2],[0,4,3]]*[[1,2,−3],[0,1,2],[−1,2,0]]=[[0,6,1],[−2,5,2],[−3,10,8]]

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