Cov Lus Nug Piv Txwv Sib Tham Txog Cov Txheej Txheem ntawm Cov Kab Ke thiab Cov Kev Tsis Sib Npaug
Cov kab ke ntawm cov kab zauv linear thiab cov kab zauv tsis sib npaug yog ib qho tseem ceeb hauv kev kawm lej uas siv dav hauv ntau qhov chaw, xws li kev lag luam, kev tshawb fawb, thiab kev tsim kho. Hauv tsab xov xwm no, peb yuav tham txog cov teeb meem piv txwv uas cuam tshuam nrog cov kab ke ntawm cov kab zauv linear thiab cov kab zauv tsis sib npaug thiab yuav daws lawv li cas kom meej.
Kev Txhais Lus ntawm Ib Lub System of Linear Equations
Ib qho system ntawm cov kab zauv linear muaj ob lossis ntau dua cov kab zauv linear uas muaj feem cuam tshuam rau ib leeg. Piv txwv li:
\[
\begin{cov ntaub ntawv}
2x + 3y = 5 \\
4x – y = 1
\end{cases}
\]
Lub hom phiaj ntawm kev daws qhov system no yog nrhiav cov nqi ntawm \(x\) thiab \(y\) uas ua tiav ob qho kev sib npaug tib lub sijhawm.
Cov Txheej Txheem rau Kev Daws Cov Kab Ke ntawm Cov Kab Ke Linear
Muaj ntau txoj kev los daws cov kab ke ntawm cov kab zauv linear, suav nrog:
1. Txoj Kev Hloov Chaw
2. Txoj Kev Tshem Tawm
3. Txoj Kev Matrix (Inverse lossis Gauss-Jordan)
Piv txwv lus nug 1: Txoj kev hloov pauv
Cia peb daws cov teeb meem hauv qab no siv txoj kev hloov pauv:
\[
\begin{cov ntaub ntawv}
x + 2y = 10 \\
3x – y = 5
\end{cases}
\]
Cov Kauj Ruam:
1. Cais ib qho ntawm cov hloov pauv hauv ib qho ntawm cov qauv.
Los ntawm thawj kab zauv, peb cais \(x\):
\[
x = 10 – 2y
\]
2. Hloov cov lus qhia pom rau hauv lwm qhov kev sib npaug.
Hloov \(x = 10 – 2y\) rau hauv kab zauv thib ob:
\[
3(10 – 2y) – y = 5
\]
Daws rau \(y\):
\[
30 – 6 xyoo – xyoo = 5
\]
\[
30 – 7 xyoo = 5
\]
\[
-7 xyoo = -25
\]
\[
y = \frac{25}{7}
\]
3. Siv cov nqi uas pom los nrhiav lwm cov hloov pauv.
Hloov \(y = \frac{25}{7}\) rov qab rau hauv kab lus rau \(x\):
\[
x = 10 – 2\sab laug (\frac{25}{7}\right)
\]
\[
x = 10 – 50 {\frac{7}}
\]
\[
x = \frac{70}{7} – \frac{50}{7}
\]
\[
x = \frac{20}{7}
\]
Yog li, cov lus teb rau lub system yog \( x = \frac{20}{7} \) thiab \( y = \frac{25}{7} \).
Piv txwv lus nug 2: Txoj kev tshem tawm
Tom ntej no, cia peb siv txoj kev tshem tawm los daws qhov system hauv qab no:
\[
\begin{cov ntaub ntawv}
2x + 3y = 12 \\
4x + 6y = 24
\end{cases}
\]
Hauv qhov no, peb pom tias qhov sib npaug thib ob yog tus lej ntau ntawm thawj qhov sib npaug. Txhawm rau kom txo qhov system, peb tuaj yeem muab thawj qhov sib npaug los ntawm 2 thiab tom qab ntawd rho tawm ntawm qhov sib npaug thib ob:
1. Muab thawj kab zauv los ntawm 2:
\[
2(2x + 3y) = 2 x 12
\]
\[
4x + 6y = 24
\]
2. Rho tawm qhov sib npaug thawj zaug uas tau muab sib npaug ntawm qhov sib npaug thib ob:
\[
(4x + 6y) – (4x + 6y) = 24 – 24
\]
\[
0 = 0
\]
Qhov no muab \(0 = 0\), uas qhia tau hais tias lub kaw lus muaj cov kev daws teeb meem tsis kawg thiab cov kab zauv no yog nyob ntawm.
Piv txwv lus nug 3: Linear Inequalities
Cov kev tsis sib luag linear ua raws li cov ntsiab cai zoo sib xws rau cov kab zauv linear, tab sis muaj cov cim tsis sib luag xws li \(<, \leq, >, \geq\). Cia peb saib ib qho piv txwv yooj yim:
\[
\begin{cov ntaub ntawv}
3x – y < 7 \\ 2x + y \geq 4 \end{cases} \] Cov Kauj Ruam: 1. Peb siv txoj kev kos duab los txiav txim siab thaj chaw daws teeb meem ntawm lub kaw lus no. Kos duab txhua qhov tsis sib xws. 2. Hloov qhov tsis sib xws mus rau hauv ib qho kab zauv los txiav txim siab txoj kab ciam teb: Rau \(3x - y < 7\), txoj kab ciam teb yog \(3x - y = 7\)
