Multiply the Matrices [[1,1],[2,1]]*[[1],[1]]

Problem

[[1,1],[2,1]]*[[1],[1]]

Solution

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

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

1*(1)+1*(1)=2

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

2*(1)+1*(1)=3

4. Assemble the resulting values into a new column matrix.

[[2],[3]]

Final Answer

[[1,1],[2,1]]*[[1],[1]]=[[2],[3]]

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