1.3.1: Ejercicios 1.3
- Page ID
- 116485
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)En Ejercicios\(\PageIndex{1}\) -\(\PageIndex{4}\), indiquen si las matrices dadas están o no en forma de escalón de fila reducida. Si no lo es, indícales por qué.
- \(\left[\begin{array}{cc}{1}&{0}\\{0}&{1}\end{array}\right]\)
- \(\left[\begin{array}{cc}{0}&{1}\\{1}&{0}\end{array}\right]\)
- \(\left[\begin{array}{cc}{1}&{1}\\{1}&{1}\end{array}\right]\)
- \(\left[\begin{array}{ccc}{1}&{0}&{1}\\{0}&{1}&{2}\end{array}\right]\)
- Contestar
-
- si
- no
- no
- si
- \(\left[\begin{array}{ccc}{1}&{0}&{0}\\{0}&{0}&{1}\end{array}\right]\)
- \(\left[\begin{array}{ccc}{1}&{0}&{1}\\{0}&{1}&{1}\end{array}\right]\)
- \(\left[\begin{array}{ccc}{0}&{0}&{0}\\{1}&{0}&{0}\end{array}\right]\)
- \(\left[\begin{array}{ccc}{0}&{0}&{0}\\{0}&{0}&{0}\end{array}\right]\)
- Contestar
-
- si
- si
- no
- si
- \(\left[\begin{array}{ccc}{1}&{1}&{1}\\{0}&{1}&{1}\\{0}&{0}&{1}\end{array}\right]\)
- \(\left[\begin{array}{ccc}{1}&{0}&{0}\\{0}&{1}&{0}\\{0}&{0}&{0}\end{array}\right]\)
- \(\left[\begin{array}{ccc}{1}&{0}&{0}\\{0}&{0}&{1}\\{0}&{0}&{0}\end{array}\right]\)
- \(\left[\begin{array}{cccc}{1}&{0}&{0}&{-5}\\{0}&{1}&{0}&{7}\\{0}&{0}&{1}&{3}\end{array}\right]\)
- Contestar
-
- no
- si
- si
- si
- \(\left[\begin{array}{cccc}{2}&{0}&{0}&{2}\\{0}&{2}&{0}&{2}\\{0}&{0}&{2}&{2}\end{array}\right]\)
- \(\left[\begin{array}{cccc}{0}&{1}&{0}&{0}\\{0}&{0}&{1}&{0}\\{0}&{0}&{0}&{0}\end{array}\right]\)
- \(\left[\begin{array}{cccc}{0}&{0}&{1}&{-5}\\{0}&{0}&{0}&{0}\\{0}&{0}&{0}&{0}\end{array}\right]\)
- \(\left[\begin{array}{cccccc}{1}&{1}&{0}&{0}&{1}&{1}\\{0}&{0}&{1}&{0}&{1}&{1}\\{0}&{0}&{0}&{1}&{0}&{0}\end{array}\right]\)
- Contestar
-
- no
- si
- si
- si
En Ejercicios\(\PageIndex{5}\) -\(\PageIndex{22}\), usa Eliminación Gaussiana para poner la matriz dada en forma de escalón de fila reducida.
\(\left[\begin{array}{cc}{1}&{2}\\{-3}&{-5}\end{array}\right]\)
- Contestar
-
\(\left[\begin{array}{cc}{1}&{0}\\{0}&{1}\end{array}\right]\)
\(\left[\begin{array}{cc} 2&-2\\3&-2\end{array}\right]\)
- Contestar
-
\(\left[\begin{array}{cc} 1&0\\0&1\end{array}\right]\)
\(\left[\begin{array}{cc} 4&12\\-2&-6\end{array}\right]\)
- Contestar
-
\(\left[\begin{array}{cc} 1&3\\0&0\end{array}\right]\)
\(\left[\begin{array}{cc} -5&7\\10&14\end{array}\right]\)
- Contestar
-
\(\left[\begin{array}{cc} 1&-7/5\\0&0\end{array}\right]\)
\(\left[\begin{array}{ccc} -1&1&4\\-2&1&1\end{array}\right]\)
- Contestar
-
\(\left[\begin{array}{ccc} 1&0&3\\0&1&7\end{array}\right]\)
\(\left[\begin{array}{ccc} 7&2&3\\3&1&2\end{array}\right]\)
- Contestar
-
\(\left[\begin{array}{ccc} 1&0&-1\\0&1&5\end{array}\right]\)
\(\left[\begin{array}{ccc} 3&-3&6\\-1&1&-2\end{array}\right]\)
- Contestar
-
\(\left[\begin{array}{ccc} 1&-1&2\\0&0&0\end{array}\right]\)
\(\left[\begin{array}{ccc} 4&5&-6\\-12&-15&18\end{array}\right]\)
- Contestar
-
\(\left[\begin{array}{ccc} 1&\frac54&-\frac32\\0&0&0\end{array}\right]\)
\(\left[\begin{array}{ccc} -2&-4&-8\\-2&-3&-5\\ 2&3&6\end{array}\right]\)
- Contestar
-
\(\left[\begin{array}{ccc} 1&0&0\\0&1&0\\0&0&1\end{array}\right]\)
\(\left[\begin{array}{ccc} 2&1&1\\1&1&1\\2&1&2\end{array}\right]\)
- Contestar
-
\(\left[\begin{array}{ccc} 1&0&0\\0&1&0\\0&0&1\end{array}\right]\)
\(\left[\begin{array}{ccc} 1&2&1\\1&3&1\\-1&-3&0\end{array}\right]\)
- Contestar
-
\(\left[\begin{array}{ccc} 1&0&0\\0&1&0\\0&0&1\end{array}\right]\)
\(\left[\begin{array}{ccc} 1&2&3\\0&4&5\\1&6&9\end{array}\right]\)
- Contestar
-
\(\left[\begin{array}{ccc} 1&0&0\\0&1&0\\0&0&1\end{array}\right]\)
\(\left[\begin{array}{cccc} 1&1&1&2\\2&-1&-1&1\\-1&1&1&0\end{array}\right]\)
- Contestar
-
\(\left[\begin{array}{cccc} 1&0&0&1\\0&1&1&1\\0&0&0&0\end{array}\right]\)
\(\left[\begin{array}{cccc} 2&-1&1&5\\3&1&6&-1\\3&0&5&0\end{array}\right]\)
- Contestar
-
\(\left[\begin{array}{cccc} 1&0&0&5\\0&1&0&2\\0&0&1&-3\end{array}\right]\)
\(\left[\begin{array}{cccc} 1&1&-1&7\\2&1&0&10\\3&2&-1&17\end{array}\right]\)
- Contestar
-
\(\left[\begin{array}{cccc} 1&0&1&3\\0&1&-2&4\\0&0&0&0\end{array}\right]\)
\(\left[\begin{array}{cccc} 4&1&8&15\\1&1&2&7\\3&1&5&11\end{array}\right]\)
- Contestar
-
\(\left[\begin{array}{cccc} 1&0&3&4\\0&1&-1&3\\0&0&0&0\end{array}\right]\)
\(\left[\begin{array}{cccccc} 2&2&1&3&1&4\\1&1&1&3&1&4\end{array}\right]\)
- Contestar
-
\(\left[\begin{array}{cccccc} 1&1&0&0&0&0\\0&0&1&3&1&4\end{array}\right]\)
\(\left[\begin{array}{cccccc} 1&-1&3&1&-2&9\\2&-2&6&1&-2&13\end{array}\right]\)
- Contestar
-
\(\left[\begin{array}{cccccc} 1&-1&3&0&0&4\\0&0&0&1&-2&5\end{array}\right]\)