Simplify the Matrix [[1,0],[0,4]][[5,2,-1],[2,-1,2]]

Problem

[[1,0],[0,4]]*[[5,2,−1],[2,−1,2]]

Solution

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

2. Calculate the first row of the product by multiplying the first row of the left matrix by each column of the right matrix.

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

1*(2)+0*(−1)=2

1*(−1)+0*(2)=−1

3. Calculate the second row of the product by multiplying the second row of the left matrix by each column of the right matrix.

0*(5)+4*(2)=8

0*(2)+4*(−1)=−4

0*(−1)+4*(2)=8

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

Final Answer

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

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