Multiply the Matrices [[1/2,1/2],[1/4,-1/4]][[3],[-1]]

Problem

[[1/2,1/2],[1/4,−1/4]]*[[3],[−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 resulting in 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.

1/2*(3)+1/2*(−1)

3. Simplify the arithmetic for the first entry.

3/2−1/2=2/2=1

4. 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.

1/4*(3)+(−1/4)*(−1)

5. Simplify the arithmetic for the second entry.

3/4+1/4=4/4=1

Final Answer

[[1/2,1/2],[1/4,−1/4]]*[[3],[−1]]=[[1],[1]]

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