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

Problem

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

Solution

1. Identify the dimensions of the matrices. The first matrix is a 2×1 column vector and the second matrix is a 1×2 row vector.

2. Determine the size of the resulting matrix. Since we are multiplying a 2×1 matrix by a 1×2 matrix, the result will be a 2×2 matrix.

3. Calculate each element (c_i*j) by multiplying the ith row of the first matrix by the jth column of the second matrix.

4. Compute the first row: (c_11)=2⋅3=6 and (c_12)=2⋅2=4

5. Compute the second row: (c_21)=1⋅3=3 and (c_22)=1⋅2=2

Final Answer

[[2],[1]]*[[3,2]]=[[6,4],[3,2]]

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