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Solution. Recall our definition of row-vector-matrix multiplication via dot products.

Using our definition, let's first check if our inner dimensions agree.

• The inner dimensions agree.
• The outer dimensions provide our dimensions for output vector $\overrightarrow{b}$.

Now that we know the inner dimensions agree, we can generate our first output of $\overrightarrow{b}$.

We continue this process until $m=3$.

Finally, we can place each of our entry values into the appropriate column to form the vector