Solve the Problem $V$ Is the Line $y = x$ In The $x y$

question 36

Multiple Choice

Solve the problem.
-Determine which of the following sets is a vector space. $V$ is the line $y = x$ in the $x y$ -plane: $V = \left\{ \left[ \begin{array} { l } x \\ y \end{array} \right] : y = x \right\}$
$W$ is the union of the first and second quadrants in the xy-plane: $W = \left\{ \left[ \begin{array} { l } x \\ y \end{array} \right] : y \geq 0 \right\}$ $U$ is the line $y = x + 1$ in the $x y$ -plane: $U = \left\{ \left[ \begin{array} { l } x \\ y \end{array} \right] : y = x + 1 \right\}$

• A) \(W\) only
• B) \(U\) and \(V\)
• C) V only
• D) \(U\) only

---

Definitions:

Collected Data

Information that has been gathered through observation, experimentation, surveys, or other methodologies for analysis and decision-making.

Specific Actions

Detailed steps or measures to be taken in order to achieve a particular goal or resolve an issue.

Decision Matrix

A tool used to compare and prioritize a list of options or variables based on a set of criteria.

Problem-Solving Model

A systematic process used to identify, analyze, and solve problems, often involving steps such as problem identification, solution brainstorming, and implementation.