Question

(Compute the dot products in Exercises 10 through 12

if the products are defined)

10.

$\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right]\mathbf{}\mathbf{,}\mathbf{}\left[\begin{array}{c}1\\ -2\\ 1\end{array}\right]$

Short answer

The dot product of $\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right],\left[\begin{array}{c}1\\ -2\\ 1\end{array}\right]$is not defined.

Step-by-step solution

Step 1:

No steps as the dot product is not possible.

For the first matrix $\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right]$

The number of rows

m=3

For the second matrix$\left[\begin{array}{c}1\\ -2\\ 1\end{array}\right]$

The number of columns

n=1

We can see thatm≠n.

Hence, dot product is not possible.

Final answer:

The dot product of $\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right],\left[\begin{array}{c}1\\ -2\\ 1\end{array}\right]$is not defined.