Algebra Archive: Questions from April 16, 2023
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(i) \( \left[\begin{array}{lll}k & 1 & 1\end{array}\right]\left[\begin{array}{ccc}1 & 1 & 0 \\ 1 & 0 & 2 \\ 0 & 2 & -3\end{array}\right]\left[\begin{array}{l}k \\ 1 \\ 1\end{array}\right]=0 \) (ii) \(2 answers -
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Given: \( \quad T: R^{3} \rightarrow R^{3}, \quad T(x, y, z)=(x+2 y, y+2 z, z+2 x) \) Find: (a) \( \operatorname{ker}(T) \) (b) \( \operatorname{nullity}(T) \) (c) range( \( T) \) (d) \( \operatorname2 answers -
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