Multiply the Matrices [[2,3],[1,-5]][[4],[1]]

Problem

[[2,3],[1,−5]]*[[4],[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 result by taking the dot product of the first row of the left matrix and the column of the right matrix.

2*(4)+3*(1)=8+3=11

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

1*(4)+(−5)*(1)=4−5=−1

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

Final Answer

[[2,3],[1,−5]]*[[4],[1]]=[[11],[−1]]

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