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

Problem

[[0,1],[1,0]]*[[2],[−1]]

Solution

1. Identify the dimensions of the matrices to ensure multiplication is defined. The first matrix is 2×2 and the second is 2×1 so the result will be a 2×1 matrix.

2. Calculate the first entry of the resulting matrix by taking the dot product of the first row of the left matrix and the column of the right matrix.

0*(2)+1*(−1)=−1

3. Calculate the second entry of the resulting matrix by taking the dot product of the second row of the left matrix and the column of the right matrix.

1*(2)+0*(−1)=2

4. Combine the results into the final column vector.

[[−1],[2]]

Final Answer

[[0,1],[1,0]]*[[2],[−1]]=[[−1],[2]]

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