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

Problem

[[2],[−3],[1]]*[[2,−3,1]]

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 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.

3. Calculate the first row of the product matrix:

2⋅2=4

2⋅−3=−6

2⋅1=2

4. Calculate the second row of the product matrix:

−3⋅2=−6

−3⋅−3=9

−3⋅1=−3

5. Calculate the third row of the product matrix:

1⋅2=2

1⋅−3=−3

1⋅1=1

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

Final Answer

[[2],[−3],[1]]*[[2,−3,1]]=[[4,−6,2],[−6,9,−3],[2,−3,1]]

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