A fire investigator arrives on the scene of a retail store f…
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?
Read DetailsLet 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.
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