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).

(Worth 8 points total) Solve the matrix equation below for the unknown \(2\times 2\) matrix \(X\): \( X \begin{bmatrix} 1 & 2 \\ 0 & 1 \end{bmatrix} – \begin{bmatrix} 1 & 0 \\ 0 & 3 \end{bmatrix} = \begin{bmatrix} 0 & 2 \\ 2 & -1 \end{bmatrix} \) Write your final answer in the text box below. Your written work will be submitted to Gradescope as soon as you submit on Canvas.

(Worth 13 points total) Let \(A = \begin{bmatrix} 1 & -1 & 2 \\ 2 & -3 & 4 \\ 0 & -2 & 5\end{bmatrix}\)    Part A) Find the inverse of \(A\) by row reducing \([A\,|\,I]\). You must write which row operation(s) you are using at each step.   Part B) Use your \(A^{-1}\) from Part (a) to solve the following system. Simplify your final answer. \(\begin{align*} x – y + 2z &= 1 \\ 2x – 3y + 4z &= -3 \\ 5z – 2y &= 2\end{align*}\)   Write your final answers in the text box below. Your written work will be submitted to Gradescope as soon as you submit on Canvas.

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.

The old painting depicted a ______ creature with twisted limbs and an unsettling grin, making everyone in the room uneasy.

He was ______ with the responsibility of caring for his sick father while juggling his demanding job.