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.   

If I violate any exam rules and do not follow the exam directions, I understand that I will receive a zero for the exam and will be reported for a violation of Academic Misconduct.

Your Practice Exam, Midterm and Final Exams sessions are recorded for Professor Porter to view and she watches all of them to make sure you are using academic honesty throughout your test.  

What would be consider a good place to take our Exams. (Check all that apply)

When 2610 + 11.7 + 0.22 is calculated, the answer to the correct number of decimal places is ________.  

The average distance from Earth to the moon is 238,900 miles. How far is this in kilometers? Express your answer in scientific notation and use the proper number of significant figures and units. (1 mile = 1,609.344 meters)