Multiply the Matrices [[-3,0],[2,-5],[-7,4]][[1,0,1],[0,1,1]]

Problem

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

Solution

1. Identify the dimensions of the matrices to ensure multiplication is possible. The first matrix is 3×2 and the second is 2×3 Since the number of columns in the first equals the number of rows in the second, the resulting matrix will be 3×3

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.

(−3)*(1)+(0)*(0)=−3

(−3)*(0)+(0)*(1)=0

(−3)*(1)+(0)*(1)=−3

3. 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.

(2)*(1)+(−5)*(0)=2

(2)*(0)+(−5)*(1)=−5

(2)*(1)+(−5)*(1)=−3

4. 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.

(−7)*(1)+(4)*(0)=−7

(−7)*(0)+(4)*(1)=4

(−7)*(1)+(4)*(1)=−3

5. Assemble the calculated values into the final 3×3 matrix.

Final Answer

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

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