A fire investigator arrives on the scene of a retail store fire and determines the smoke and steam are too heavy to conduct a proper investigation. The investigator returns the next morning and conducts the investigation, finding no evidence. One week later, the investigator returns again and finds several items of significant evidence. Will this evidence be permitted for use in court?

What is a common cause of decreased water volume in older distribution systems?

Considering a high-rise operation, where should rehab be established?

A fire can only be deemed fully extinguished when what has been completed?

What was one conclusion of the Paris study on victims of smoke inhalation?

In which occupancy type do most civilian deaths occur due to fire?

Reduce the matrix A below to the Reduced Row Echelon Form, showing all the steps. $$\left[ \begin{array}{rrrr}1 & 0 & 1 & -1 \\0 & -1 & -3 & 4 \\3 & 0 & 3 & -3 \\-3 & 0 & -3 & -1 \\\end{array} \right]$$

Let T be a linear transformation. Define $$T: R^4 \rightarrow R^3$$ by $$T \left(\begin{bmatrix}&1 \\&0\\&0\\&0\end{bmatrix} \right) = \begin{bmatrix}&2\\&3\\&0\end{bmatrix} $$, $$T \left(\begin{bmatrix}&0 \\&1\\&0\\&0\end{bmatrix} \right) = \begin{bmatrix}&0\\&2\\&1\end{bmatrix} $$, $$T \left(\begin{bmatrix}&0 \\&0\\&1\\&0\end{bmatrix} \right) = \begin{bmatrix}&6\\&1\\&2\end{bmatrix} $$, $$T \left(\begin{bmatrix}&0 \\&0\\&0\\&1\end{bmatrix} \right) = \begin{bmatrix}&0\\&3\\&0\end{bmatrix} $$   a) Using the information above, find a formula for $$T(\vec{x})$$ for all $$\vec{x} = \begin{bmatrix}&x_1 \\&x_2\\&x_3\\&x_4\end{bmatrix} $$ in $$R^4$$.   b) Find the standard matrix A of T.   c) Is T one-to-one? Prove your answer using the matrix A.   d) Is T onto? Prove your answer using the matrix A.  

Part 2 – InstructionsOn the next five problems, SHOW ALL WORK.  After you submit your test, take pictures of your work for the five problems below and upload them to Canvas using the link “TEST 1 Work” that is underneath the link for this test in Canvas.  Make sure that you show all work and write neatly and darkly enough for me to read it.  If I can’t see or read your work, I cannot give you any credit.   Please be sure to submit your work for these problems in “Test 1 Work” in the TEST REVIEW AND TEST MODULE by 8:00 am May 31, 2025.

I conducted a slow, thorough, 360 degree room scan to show that my desk is cleared away, I only have 1 computer monitor on my desk, and that there are no other people with me in my testing space.  My scan also shows that I do not have any other electronic devices around me, nothing is on my wrists or in my ears.