Add [[3],[5],[1],[7]]*[[3,5,1,7]]

Problem

[[3],[5],[1],[7]]*[[3,5,1,7]]

Solution

1. Identify the operation as the outer product of a 4×1 column vector and a 1×4 row vector.

2. Determine the dimensions of the resulting matrix, which will be a 4×4 matrix where each element (a_i*j) is the product of the ith element of the first vector and the jth element of the second vector.

3. Calculate the first row by multiplying the first element of the column vector (3) by each element of the row vector.

3×[[3,5,1,7]]=[[9,15,3,21]]

4. Calculate the second row by multiplying the second element of the column vector (5) by each element of the row vector.

5×[[3,5,1,7]]=[[15,25,5,35]]

5. Calculate the third row by multiplying the third element of the column vector (1) by each element of the row vector.

1×[[3,5,1,7]]=[[3,5,1,7]]

6. Calculate the fourth row by multiplying the fourth element of the column vector (7) by each element of the row vector.

7×[[3,5,1,7]]=[[21,35,7,49]]

7. Assemble the rows into the final 4×4 matrix.

Final Answer

[[3],[5],[1],[7]]*[[3,5,1,7]]=[[9,15,3,21],[15,25,5,35],[3,5,1,7],[21,35,7,49]]

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