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

Problem

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

Solution

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

2. Apply the matrix multiplication rule where the element in the ith row and jth column is the product of the ith element of the first matrix and the jth element of the second matrix.

3. Calculate the first row of the product:

3⋅3=9

3⋅1=3

3⋅3=9

4. Calculate the second row of the product:

2⋅3=6

2⋅1=2

2⋅3=6

5. Calculate the third row of the product:

1⋅3=3

1⋅1=1

1⋅3=3

6. Assemble the results into the final 3×3 matrix.

Final Answer

[[3],[2],[1]]*[[3,1,3]]=[[9,3,9],[6,2,6],[3,1,3]]

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