All children benefit from being in an organized and consistent environment with rituals and routines.

Dishes in the housekeeping area should be washed monthly.

The YWCA provides opportunities based on the child’s age, but can include camping, matchbox cars, and community service projects.

Linoleum flooring is an undesirable flooring option due to its lack of durability.

Where can a list of types of equipment and materials required for each age group be found?

What is the purpose of having groups of similar-aged children in the same area when planning room arrangements?

Home-based programs will not have state-mandated practices or expectations.

A laundry basket may serve as an excellent collection tool when disinfecting toys.

(Worth 5 points total) For the matrix \(A = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 5 & 8 \end{bmatrix}\), find its nullspace \(N(A)\).   Write your final answers in the text box below. Your written work will be submitted to Gradescope as soon as you submit on Canvas.

(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).