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

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