Multiply the Matrices [[2,1],[3,2]][[1],[3]]

Problem

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

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.

2*(1)+1*(3)=2+3=5

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.

3*(1)+2*(3)=3+6=9

4. Assemble the results into the final column matrix.

[[5],[9]]

Final Answer

[[2,1],[3,2]]*[[1],[3]]=[[5],[9]]

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