Multiply the Matrices [[2,3],[4,5]]*[[2],[3]]

Problem

[[2,3],[4,5]]*[[2],[3]]

Solution

1. Identify the dimensions of the matrices to ensure multiplication is possible. 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 by taking the dot product of the first row of the left matrix and the column of the right matrix.

2*(2)+3*(3)=4+9=13

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

4*(2)+5*(3)=8+15=23

4. Combine the results into the final column matrix.

Final Answer

[[2,3],[4,5]]*[[2],[3]]=[[13],[23]]

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