Multiply the Matrices

Problem

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

Solution

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

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

(c_11)=(1)*(−2)+(0)*(1)+(3)*(−1)=−2+0−3=−5

(c_12)=(1)*(4)+(0)*(0)+(3)*(1)=4+0+3=7

(c_13)=(1)*(2)+(0)*(0)+(3)*(1)=2+0+3=5

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

(c_21)=(2)*(−2)+(−1)*(1)+(−2)*(−1)=−4−1+2=−3

(c_22)=(2)*(4)+(−1)*(0)+(−2)*(1)=8+0−2=6

(c_23)=(2)*(2)+(−1)*(0)+(−2)*(1)=4+0−2=2

4. Assemble the resulting matrix using the calculated values.

Final Answer

[[1,0,3],[2,−1,−2]]*[[−2,4,2],[1,0,0],[−1,1,1]]=[[−5,7,5],[−3,6,2]]

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