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

Problem

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

Solution

1. Identify the dimensions of the matrices to ensure they can be multiplied. The first matrix is 3×2 and the second is 2×2 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 the columns of the right matrix.

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

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

3. Calculate the second row of the product by taking the dot product of the second row of the left matrix with the columns of the right matrix.

2*(5)+3*(1)=13

2*(4)+3*(2)=14

4. Calculate the third row of the product by taking the dot product of the third row of the left matrix with the columns of the right matrix.

4*(5)+5*(1)=25

4*(4)+5*(2)=26

5. Assemble the results into the final 3×2 matrix.

Final Answer

[[0,1],[2,3],[4,5]]*[[5,4],[1,2]]=[[1,2],[13,14],[25,26]]

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