Multiply the Matrices

Problem

[[√(,2)/2],[√(,2)/2],[0]]*[[√(,2)/2,√(,2)/2,0]]

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 product will be a 3×3 matrix.

2. 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.

3. Calculate the elements for the first row:

√(,2)/2⋅√(,2)/2=2/4=1/2

√(,2)/2⋅√(,2)/2=1/2

√(,2)/2⋅0=0

4. Calculate the elements for the second row:

√(,2)/2⋅√(,2)/2=1/2

√(,2)/2⋅√(,2)/2=1/2

√(,2)/2⋅0=0

5. Calculate the elements for the third row:

0⋅√(,2)/2=0

0⋅√(,2)/2=0

0⋅0=0

6. Assemble the resulting 3×3 matrix using the calculated values.

Final Answer

[[√(,2)/2],[√(,2)/2],[0]]*[[√(,2)/2,√(,2)/2,0]]=[[1/2,1/2,0],[1/2,1/2,0],[0,0,0]]

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