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

Problem

[[−1],[2],[1]]*[[2,3,−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 matrix multiplication rule 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⋅3=−3

−1⋅−1=1

5. Calculate the second row:

2⋅2=4

2⋅3=6

2⋅−1=−2

6. Calculate the third row:

1⋅2=2

1⋅3=3

1⋅−1=−1

Final Answer

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

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