Simplify the Matrix [[-1,0],[0,-1]][[x],[y]]

Problem

[[−1,0],[0,−1]]*[[x],[y]]

Solution

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

2. Apply the rule for matrix multiplication by multiplying the rows of the first matrix by the column of the second matrix.

3. Calculate the first entry of the resulting matrix by taking the dot product of the first row and the column.

(−1)*(x)+(0)*(y)=−x

4. Calculate the second entry of the resulting matrix by taking the dot product of the second row and the column.

(0)*(x)+(−1)*(y)=−y

5. Combine the results into a single column matrix.

Final Answer

[[−1,0],[0,−1]]*[[x],[y]]=[[−x],[−y]]

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