1.1.1: Ejercicios 1.1
- Page ID
- 116452
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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\(\PageIndex{1}\) -\(\PageIndex{10}\), indique si la ecuación dada es lineal o no.
\(x+y+z = 10\)
- Contestar
-
Lineal
\(xy + yz+ xz = 1\)
- Contestar
-
No lineal
\(-3x + 9 = 3y - 5z+ x-7\)
- Contestar
-
Lineal
\(\sqrt{5}y + \pi x =-1\)
- Contestar
-
Lineal
\((x-1)(x+1) = 0\)
- Contestar
-
No lineal
\(\sqrt{x_1^2+x_2^2} = 25\)
- Contestar
-
No lineal
\(x_1 + y + t = 1\)
- Contestar
-
Lineal
\(\frac{1}{x} + 9 = 3\cos(y) - 5z\)
- Contestar
-
No lineal
\(\cos(15)y + \frac{x}{4} =-1\)
- Contestar
-
Lineal
\(2^x + 2^y = 16\)
- Contestar
-
No lineal
En Ejercicios\(\PageIndex{11}\) -\(\PageIndex{14}\), resolver el sistema de ecuaciones lineales.
\(\begin{array}{ccccc} x&+&y&=&-1\\ 2x&-&3y&=&8\\ \end{array}\)
- Contestar
-
\(x = 1, y=-2\)
\(\begin{array}{ccccc} 2x&-&3y&=&3\\ 3x&+&6y&=&8\\ \end{array}\)
- Contestar
-
\(x = 2, y=\frac13\)
\(\begin{array}{ccccccc} x&-&y&+&z&=&1\\ 2x&+&6y&-&z&=&-4\\ 4x&-&5y&+&2z&=&0\\ \end{array}\)
- Contestar
-
\(x = -1, y=0,z=2\)
\(\begin{array}{ccccccc} x&+&y&-&z&=&1\\ 2x&+&y&&&=&2\\ &&y&+&2z&=&0\\ \end{array}\)
- Contestar
-
\(x =1,\ y=0,\ z=0\)
Un granjero mira por su ventana a sus gallinas y cerdos. Le dice a su hija que ve 62 cabezas y 190 piernas. ¿Cuántos pollos y cerdos tiene el granjero?
- Contestar
-
29 pollos y 33 cerdos
Una señora compra 20 baratijas en una venta de patio. El costo de cada baratija es de $0.30 o $0.65. Si gasta 8.80 dólares, ¿cuántos de cada tipo de baratija compra?
- Contestar
-
12 $0.30 baratijas, 8 $0.65 baratijas