Arizona State University (ASU) MAT343 Applied Linear Algebra Exam 2 Practice

The dot product of two vectors is computed by summing the products of their corresponding components. This method involves taking each pair of corresponding elements from the two vectors, multiplying them together, and then adding all those products together to yield a single scalar value.

For example, if you have two vectors \( \mathbf{u} = [u_1, u_2] \) and \( \mathbf{v} = [v_1, v_2] \), the dot product \( \mathbf{u} \cdot \mathbf{v} \) is calculated as:

\[

\mathbf{u} \cdot \mathbf{v} = u_1 v_1 + u_2 v_2

\]

This operation captures the degree of parallelism between the vectors and can also be interpreted geometrically. The dot product can be related to the angle \( \theta \) between two vectors through the formula \( \| \mathbf{u} \| \| \mathbf{v} \| \cos(\theta) \), but this is more about understanding the relationship between the vectors rather than a direct computation of the dot product.

The other options describe different concepts and not the process of calculating the