2.5.1: Ejercicios 2.5
- Page ID
- 116459
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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\(\PageIndex{1}\) -\(\PageIndex{12}\),\(B\) se dan matrices\(A\) y. Resolver la ecuación matricial\(AX=B\).
\(A=\left[\begin{array}{cc}{4}&{-1}\\{-7}&{5}\end{array}\right],\)
\(B=\left[\begin{array}{cc}{8}&{-31}\\{-27}&{38}\end{array}\right]\)
- Contestar
-
\(X=\left[\begin{array}{cc}{1}&{-9}\\{-4}&{-5}\end{array}\right]\)
\(A=\left[\begin{array}{cc}{1}&{-3}\\{-3}&{6}\end{array}\right],\)
\(B=\left[\begin{array}{cc}{12}&{-10}\\{-27}&{27}\end{array}\right]\)
- Contestar
-
\(X=\left[\begin{array}{cc}{3}&{-7}\\{-3}&{1}\end{array}\right]\)
\(A=\left[\begin{array}{cc}{3}&{3}\\{6}&{4}\end{array}\right],\)
\(B=\left[\begin{array}{cc}{15}&{-39}\\{16}&{-66}\end{array}\right]\)
- Contestar
-
\(X=\left[\begin{array}{cc}{-2}&{-7}\\{7}&{-6}\end{array}\right]\)
\(A=\left[\begin{array}{cc}{-3}&{-6}\\{4}&{0}\end{array}\right],\)
\(B=\left[\begin{array}{cc}{48}&{-30}\\{0}&{-8}\end{array}\right]\)
- Contestar
-
\(X=\left[\begin{array}{cc}{0}&{-2}\\{-8}&{6}\end{array}\right]\)
\(A=\left[\begin{array}{cc}{-1}&{-2}\\{-2}&{-3}\end{array}\right],\)
\(B=\left[\begin{array}{ccc}{13}&{4}&{7}\\{22}&{5}&{12}\end{array}\right]\)
- Contestar
-
\(X=\left[\begin{array}{ccc}{-5}&{2}&{-3}\\{-4}&{-3}&{-2}\end{array}\right]\)
\(A=\left[\begin{array}{cc}{-4}&{1}\\{-1}&{-2}\end{array}\right],\)
\(B=\left[\begin{array}{ccc}{-2}&{-10}&{19}\\{13}&{2}&{-2}\end{array}\right]\)
- Contestar
-
\(X=\left[\begin{array}{ccc}{-1}&{2}&{-4}\\{-6}&{-2}&{3}\end{array}\right]\)
\(A=\left[\begin{array}{cc}{1}&{0}\\{3}&{-1}\end{array}\right],\quad B=I_{2}\)
- Contestar
-
\(X=\left[\begin{array}{cc}{1}&{0}\\{3}&{-1}\end{array}\right]\)
\(A=\left[\begin{array}{cc}{2}&{2}\\{3}&{1}\end{array}\right],\quad B=I_{2}\)
- Contestar
-
\(X=\left[\begin{array}{cc}{-1/4}&{1/2}\\{3/4}&{-1/2}\end{array}\right]\)
\(A=\left[\begin{array}{ccc}{-2}&{0}&{4}\\{-5}&{-4}&{5}\\{-3}&{5}&{-3}\end{array}\right],\)
\(B=\left[\begin{array}{ccc}{-18}&{2}&{-14}\\{-38}&{18}&{-13}\\{10}&{2}&{-18}\end{array}\right]\)
- Contestar
-
\(X=\left[\begin{array}{ccc}{3}&{-3}&{3}\\{2}&{-2}&{-3}\\{-3}&{-1}&{-2}\end{array}\right]\)
\(A=\left[\begin{array}{ccc}{-5}&{-4}&{-1}\\{8}&{-2}&{-3}\\{6}&{1}&{-8}\end{array}\right],\)
\(B=\left[\begin{array}{ccc}{-21}&{-8}&{-19}\\{65}&{-11}&{-10}\\{75}&{-51}&{33}\end{array}\right]\)
- Contestar
-
\(X=\left[\begin{array}{ccc}{6}&{1}&{-1}\\{-1}&{-1}&{7}\\{-5}&{7}&{-4}\end{array}\right]\)
\(A=\left[\begin{array}{ccc}{0}&{-2}&{1}\\{0}&{2}&{2}\\{1}&{2}&{-3}\end{array}\right],\quad B=I_{3}\)
- Contestar
-
\(X=\left[\begin{array}{ccc}{5/3}&{2/3}&{1}\\{-1/3}&{1/6}&{0}\\{1/3}&{1/3}&{0}\end{array}\right]\)
\(A=\left[\begin{array}{ccc}{-3}&{3}&{-2}\\{1}&{-3}&{2}\\{-1}&{-1}&{2}\end{array}\right],\quad B=I_{3}\)
- Contestar
-
\(X=\left[\begin{array}{ccc}{-1/2}&{-1/2}&{0}\\{-1/2}&{-1}&{1/2}\\{-1/2}&{-3/4}&{3/4}\end{array}\right]\)