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

Problem

[[1],[3],[1]]*[[5,−1]]

Solution

1. Identify the dimensions of the matrices. The first matrix is a 3×1 column vector and the second matrix is a 1×2 row vector.

2. Determine the size of the resulting matrix. Multiplying a 3×1 matrix by a 1×2 matrix results in a 3×2 matrix.

3. Apply the matrix multiplication rule where the element at row i and column j is the product of the ith row of the first matrix and the jth column of the second matrix.

4. Calculate the first row: 1⋅5=5 and 1⋅(−1)=−1

5. Calculate the second row: 3⋅5=15 and 3⋅(−1)=−3

6. Calculate the third row: 1⋅5=5 and 1⋅(−1)=−1

Final Answer

[[1],[3],[1]]*[[5,−1]]=[[5,−1],[15,−3],[5,−1]]

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