Multiply the Matrices [[-2,-1],[0,-1]][[-1],[1]]

Problem

[[−2,−1],[0,−1]]*[[−1],[1]]

Solution

1. Identify the dimensions of the matrices to ensure they can be multiplied. The first matrix is 2×2 and the second is 2×1 so the resulting matrix will be 2×1

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.

(−2)*(−1)+(−1)*(1)=2−1=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.

(0)*(−1)+(−1)*(1)=0−1=−1

4. Combine the calculated entries into the final 2×1 matrix.

[[1],[−1]]

Final Answer

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

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