Multiply the Matrices [[0],[3],[4]][[2,0,-1]]

Problem

[[0],[3],[4]]*[[2,0,−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 formula for matrix multiplication, 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.

3. Calculate the elements of the first row:

0⋅2=0

0⋅0=0

0⋅−1=0

4. Calculate the elements of the second row:

3⋅2=6

3⋅0=0

3⋅−1=−3

5. Calculate the elements of the third row:

4⋅2=8

4⋅0=0

4⋅−1=−4

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

Final Answer

[[0],[3],[4]]*[[2,0,−1]]=[[0,0,0],[6,0,−3],[8,0,−4]]

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