Simplify the Matrix [[0,0],[1,0]][[1,-5],[3,2]]

Problem

[[0,0],[1,0]]*[[1,−5],[3,2]]

Solution

1. Identify the dimensions of the matrices. Both are 2×2 matrices, so the resulting matrix will also be 2×2

2. Calculate the element in the first row, first column by taking the dot product of the first row of the first matrix and the first column of the second matrix.

0*(1)+0*(3)=0

3. Calculate the element in the first row, second column by taking the dot product of the first row of the first matrix and the second column of the second matrix.

0*(−5)+0*(2)=0

4. Calculate the element in the second row, first column by taking the dot product of the second row of the first matrix and the first column of the second matrix.

1*(1)+0*(3)=1

5. Calculate the element in the second row, second column by taking the dot product of the second row of the first matrix and the second column of the second matrix.

1*(−5)+0*(2)=−5

6. Assemble the resulting matrix using the calculated values.

Final Answer

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

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