Chapter 2: Q26Q (page 93)
Explain why the columns of \({A^{\bf{2}}}\) span \({\mathbb{R}^n}\) whenever the columns of Aare linearly independent.
Short Answer
The columns of \({A^2}\) are invertible, and they span \({\mathbb{R}^n}\).
Chapter 2: Q26Q (page 93)
Explain why the columns of \({A^{\bf{2}}}\) span \({\mathbb{R}^n}\) whenever the columns of Aare linearly independent.
The columns of \({A^2}\) are invertible, and they span \({\mathbb{R}^n}\).
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Generalize the idea of Exercise 21(a) [not 21(b)] by constructing a \(5 \times 5\) matrix \(M = \left[ {\begin{array}{*{20}{c}}A&0\\C&D\end{array}} \right]\) such that \({M^2} = I\). Make C a nonzero \(2 \times 3\) matrix. Show that your construction works.
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