Part 2 – InstructionsOn the next five problems, SHOW ALL WOR…

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.

Part 2 – InstructionsOn the next five problems, SHOW ALL WOR…

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.

Let T be a linear transformation. Define $$T: R^4 \rightarro…

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.  

Michelangelo’s David statue is 18½ feet tall, including the…

Michelangelo’s David statue is 18½ feet tall, including the base. Based on the fact that the density of marble stone is 160 lbs/cubic foot, a person could estimate that the statue weighs about 5,300.0 lbs, or 2,325 kg (1 kg is 1,000 g). Marble has a chemical formula of CaCO3 (calcium carbonate). In the 1750s, Joseph Black found that if calcium carbonate is heated to a temperature of over 825°C, it decomposes and releases “fixed air,” which is CO2, and produces lime (not the citrus fruit but a solid, white chemical compound). The chemical formula of lime is CaO. Write out a balanced equation for the reaction that shows CaCO3 (calcium carbonate) reacting to produce CaO (lime) and CO2 (carbon dioxide).  BYU-Approved David Statue Note: Show all work for this question for full credit. Label the question number clearly and circle or highlight all answers. You will upload your work at the end of the exam.