Multiply $1\times 3$ matrix by corresponding numbers

I believe what you are describing is called the Hadamard product. You can read about them and see some notation for using them on the Wikipedia page. https://en.wikipedia.org/wiki/Hadamard_product_(matrices)

This page uses the notation $\circ$ for the Hadamard product.

I don't know any standard matrix operation of this kind. You can rewrite the three entries of the $1\times 3$ matrices as diagonal elements of a $3 \times 3$ matrix, than perform the standard matrix multiplication.