Multiply the Matrices

Problem

[[1,2,−1],[1,3,2]]*[[1,2,−4],[7,3,6],[1,1,−1]]

Solution

1. Identify the dimensions of the matrices to ensure multiplication is possible. The first matrix is 2×3 and the second is 3×3 The resulting matrix will be 2×3

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)*(7)+(−1)*(1)=1+14−1=14

(c_12)=(1)*(2)+(2)*(3)+(−1)*(1)=2+6−1=7

(c_13)=(1)*(−4)+(2)*(6)+(−1)*(−1)=−4+12+1=9

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)=(1)*(1)+(3)*(7)+(2)*(1)=1+21+2=24

(c_22)=(1)*(2)+(3)*(3)+(2)*(1)=2+9+2=13

(c_23)=(1)*(−4)+(3)*(6)+(2)*(−1)=−4+18−2=12

4. Assemble the calculated values into the resulting 2×3 matrix.

Final Answer

[[1,2,−1],[1,3,2]]*[[1,2,−4],[7,3,6],[1,1,−1]]=[[14,7,9],[24,13,12]]

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