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

Problem

[[3],[−1],[4]]⋅[[2],[2],[0]]

Solution

1. Identify the dimensions of the matrices. The first matrix is a 3×1 column vector and the second matrix is a 3×1 column vector.

2. Determine if the operation is possible. Standard matrix multiplication A⋅B requires the number of columns in A to equal the number of rows in B Here, 1≠3 so standard matrix multiplication is not defined.

3. Interpret the operation as a dot product. In the context of two vectors of the same dimension, the multiplication usually refers to the dot product (scalar product).

4. Apply the dot product formula by multiplying corresponding components and summing the results.

3⋅2+(−1)⋅2+4⋅0

5. Calculate the individual products.

6−2+0

6. Simplify the final sum.

4

Final Answer

[[3],[−1],[4]]⋅[[2],[2],[0]]=4

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