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.