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Question-76326




Question Number 76326 by Master last updated on 26/Dec/19
Answered by benjo last updated on 26/Dec/19
using determinan Vandermon de method
$$\mathrm{using}\:\mathrm{determinan}\:\mathrm{Vandermon}\:\mathrm{de}\:\mathrm{method}\: \\ $$
Commented by Master last updated on 26/Dec/19
solution plz
$$\mathrm{solution}\:\mathrm{plz} \\ $$
Answered by john santu last updated on 26/Dec/19
using Crammer rule  N =661, N_x =1322 →x=((1322)/(661))=2  N_y =661, y=((661)/(661))=1  N_z =2644, z=((2644)/(661))=4  N_u =3305, u=((3305)/(661))=5  so by substitusi 4(4)+5−6=5t,   t=3. now we get x + y + z +u + t  =2+1+4+5+3=15
$$\mathrm{using}\:\mathrm{Crammer}\:\mathrm{rule} \\ $$$$\mathrm{N}\:=\mathrm{661},\:\mathrm{N}_{\mathrm{x}} =\mathrm{1322}\:\rightarrow\mathrm{x}=\frac{\mathrm{1322}}{\mathrm{661}}=\mathrm{2} \\ $$$$\mathrm{N}_{\mathrm{y}} =\mathrm{661},\:\mathrm{y}=\frac{\mathrm{661}}{\mathrm{661}}=\mathrm{1} \\ $$$$\mathrm{N}_{\mathrm{z}} =\mathrm{2644},\:\mathrm{z}=\frac{\mathrm{2644}}{\mathrm{661}}=\mathrm{4} \\ $$$$\mathrm{N}_{\mathrm{u}} =\mathrm{3305},\:\mathrm{u}=\frac{\mathrm{3305}}{\mathrm{661}}=\mathrm{5} \\ $$$$\mathrm{so}\:\mathrm{by}\:\mathrm{substitusi}\:\mathrm{4}\left(\mathrm{4}\right)+\mathrm{5}−\mathrm{6}=\mathrm{5t},\: \\ $$$$\mathrm{t}=\mathrm{3}.\:\mathrm{now}\:\mathrm{we}\:\mathrm{get}\:\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\:+\mathrm{u}\:+\:\mathrm{t} \\ $$$$=\mathrm{2}+\mathrm{1}+\mathrm{4}+\mathrm{5}+\mathrm{3}=\mathrm{15} \\ $$
Commented by mr W last updated on 26/Dec/19
Commented by mr W last updated on 27/Dec/19
i mean if we don′t need to know  the values for x,y,z,u,t but the  sum of them, or things like  x+2y+3z+4u+5t=? then we can   introduce a new unknown s and  add a new equation like this:  x+2y+3z+4u+5t−s=0   now we only need to determine s:  s=(N_s /N)  ⇒x+2y+3z+4u+5t=s
$${i}\:{mean}\:{if}\:{we}\:{don}'{t}\:{need}\:{to}\:{know} \\ $$$${the}\:{values}\:{for}\:{x},{y},{z},{u},{t}\:{but}\:{the} \\ $$$${sum}\:{of}\:{them},\:{or}\:{things}\:{like} \\ $$$${x}+\mathrm{2}{y}+\mathrm{3}{z}+\mathrm{4}{u}+\mathrm{5}{t}=?\:{then}\:{we}\:{can}\: \\ $$$${introduce}\:{a}\:{new}\:{unknown}\:{s}\:{and} \\ $$$${add}\:{a}\:{new}\:{equation}\:{like}\:{this}: \\ $$$${x}+\mathrm{2}{y}+\mathrm{3}{z}+\mathrm{4}{u}+\mathrm{5}{t}−{s}=\mathrm{0}\: \\ $$$${now}\:{we}\:{only}\:{need}\:{to}\:{determine}\:{s}: \\ $$$${s}=\frac{{N}_{{s}} }{{N}} \\ $$$$\Rightarrow{x}+\mathrm{2}{y}+\mathrm{3}{z}+\mathrm{4}{u}+\mathrm{5}{t}={s}\: \\ $$
Commented by benjo last updated on 27/Dec/19
how to find Ns?
$$\mathrm{how}\:\mathrm{to}\:\mathrm{find}\:\mathrm{Ns}? \\ $$
Commented by mr W last updated on 27/Dec/19
i assumed you know Cramer rule.
$${i}\:{assumed}\:{you}\:{know}\:{Cramer}\:{rule}. \\ $$
Commented by mr W last updated on 27/Dec/19
Commented by john santu last updated on 27/Dec/19
but the value x + y +z+u+t sir   not x +2y+3z+4u+5t?
$${but}\:{the}\:{value}\:{x}\:+\:{y}\:+{z}+{u}+{t}\:{sir}\: \\ $$$${not}\:{x}\:+\mathrm{2}{y}+\mathrm{3}{z}+\mathrm{4}{u}+\mathrm{5}{t}? \\ $$
Commented by mr W last updated on 27/Dec/19
you should understand me. i just  wanted to show an example if we  need to know the value of  x +2y+3z+4u+5t !!!
$${you}\:{should}\:{understand}\:{me}.\:{i}\:{just} \\ $$$${wanted}\:{to}\:{show}\:{an}\:{example}\:{if}\:{we} \\ $$$${need}\:{to}\:{know}\:{the}\:{value}\:{of} \\ $$$${x}\:+\mathrm{2}{y}+\mathrm{3}{z}+\mathrm{4}{u}+\mathrm{5}{t}\:!!! \\ $$

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