Multiply the Matrices [[4,1],[-1,2]][[-1],[1]]

Problem

[[4,1],[−1,2]]*[[−1],[1]]

Solution

1. Identify the dimensions of the matrices. The first matrix is a 2×2 matrix and the second is a 2×1 matrix. The resulting matrix will be a 2×1 matrix.

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

(4)*(−1)+(1)*(1)=−4+1=−3

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

(−1)*(−1)+(2)*(1)=1+2=3

4. Assemble the results into the final 2×1 matrix.

Final Answer

[[4,1],[−1,2]]*[[−1],[1]]=[[−3],[3]]

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