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(Solved): . 2. Let T:R3R4 be defined by T(x)=130324151514 (a) Suppose that b= ...



2. Let \( T: \mathbb{R}^{3} \rightarrow \mathbb{R}^{4} \) be defined by
\[
T(\mathbf{x})=\left(\begin{array}{ccc}
1 & -2 & 1.

2. Let be defined by (a) Suppose that . Show that is in the range of , and find so that (b) Is it possible to find a so that is not in the range of ? Why or why not?


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Solution(a): Let A=[1213?45011?35?4]. Define a linear transformation T:R3?R3 by T(x)=Ax.If b is in the range of T, then Ax=b is
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