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

Problem

[[1],[1],[−1]]*[[2,−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 1×3 row vector.

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

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

4. Calculate the first row: 1⋅2=2 1⋅−5=−5 and 1⋅1=1

5. Calculate the second row: 1⋅2=2 1⋅−5=−5 and 1⋅1=1

6. Calculate the third row: −1⋅2=−2 −1⋅−5=5 and −1⋅1=−1

Final Answer

[[1],[1],[−1]]*[[2,−5,1]]=[[2,−5,1],[2,−5,1],[−2,5,−1]]

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