Multiply the Matrices [[-3],[4],[5]]*[[1],[1],[1]]

Problem

[[−3],[4],[5]]*[[1],[1],[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. Since we are multiplying a 3×1 matrix by a 1×3 matrix, the result will be 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 row of the first matrix and the jth column of the second matrix.

4. Calculate the first row: (−3)*(1)=−3 (−3)*(1)=−3 and (−3)*(1)=−3

5. Calculate the second row: (4)*(1)=4 (4)*(1)=4 and (4)*(1)=4

6. Calculate the third row: (5)*(1)=5 (5)*(1)=5 and (5)*(1)=5

Final Answer

[[−3],[4],[5]]*[[1,1,1]]=[[−3,−3,−3],[4,4,4],[5,5,5]]

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