(Worth 10 points total) Let \(V=\mathbb{R}^2\), with the fol…

(Worth 10 points total) Let \(V=\mathbb{R}^2\), with the following addition and scalar multiplication operations on it: \(\begin{align*} \begin{bmatrix} x_1\\x_2 \end{bmatrix} + \begin{bmatrix} y_1\\y_2 \end{bmatrix} &= \begin{bmatrix} x_1+y_1\\x_2+y_2 \end{bmatrix} \text{(that is, the usual addition),} \\\alpha \odot \begin{bmatrix} x_1\\x_2 \end{bmatrix} &= \begin{bmatrix} \max\{\alpha, x_1\}\\\max\{\alpha, x_2\} \end{bmatrix},\end{align*}\) where \(\max\{a,b\}\) means to take the larger of the two numbers \(a\) and \(b\).   List TWO vector space axioms that this space \((V, +, \odot)\) violates. For each one, give an example that demonstrates the violation.   Write your final answers in the text box below (just name the axioms- your full answers with examples will be submitted to Gradescope as soon as you submit on Canvas).

There will be 25 questions. Format is multiple choice, true/…

There will be 25 questions. Format is multiple choice, true/false and short answer questions. The Respondus Lockdown browser and webcam are required. You will need a scientific calculator, printed periodic table and printed molecular shapes table. You may also have a 3″ X 5″ notecard with any handwritten notes you wish – front and back. This is a timed exam.  You will have 90 minutes to complete the exam once you open the exam.