Solving a linear system of reciprocals.Solving system of multivariable 2nd-degree polynomialsProblem with system of equationsSolving a system of equations with variables in denominator.Solving system of non-linear equations.Solving a combined system of linear and bilinear equationsSolving system of linear equations ( 4 variables, 3 equations)Solving a system of 4 non-linear equationsSolving a linear system of congruencesEasier solution for system of equations.Solve the following system of equations - (4).
Are there lenses which can give 180° fisheye circle with a cropped-frame camera?
Alternatives to Overleaf
Is this a realistic set of world maps?
Counterexample: a pair of linearly ordered sets that are isomorphic to subsets of the other, but not isomorphic between them
How to figure out whether the data is sample data or population data apart from the client's information?
Please, smoke with good manners
Solving a linear system of reciprocals.
How can Republicans who favour free markets, consistently express anger when they don't like the outcome of that choice?
How to stop co-workers from teasing me because I know Russian?
Where did the extra Pym particles come from in Endgame?
function to receive a character input and return date format (with incorrect input)
Will this character get back his Infinity Stone?
Can fracking help reduce CO2?
Help to reproduce a tcolorbox with a decoration
Is creating your own "experiment" considered cheating during a physics exam?
Why was Germany not as successful as other Europeans in establishing overseas colonies?
Mac Pro install disk keeps ejecting itself
Finding an element in array, whose index number and element value same
How to make a pipeline wait for end-of-file or stop after an error?
Unexpected email from Yorkshire Bank
What is the incentive for curl to release the library for free?
Is there any limitation with Arduino Nano serial communication distance?
Can someone publish a story that happened to you?
Stateful vs non-stateful app
Solving a linear system of reciprocals.
Solving system of multivariable 2nd-degree polynomialsProblem with system of equationsSolving a system of equations with variables in denominator.Solving system of non-linear equations.Solving a combined system of linear and bilinear equationsSolving system of linear equations ( 4 variables, 3 equations)Solving a system of 4 non-linear equationsSolving a linear system of congruencesEasier solution for system of equations.Solve the following system of equations - (4).
$begingroup$
Solve for $begincasesfrac1x +frac1y+frac1z=0\frac4x +frac3y+frac2z=5\frac3x +frac2y+frac4z=-4endcases$
I turn the equations into $begincasesyz+xz+xy=0\4yz+3xz+2xy=5xyz\3yz+2xz+4xy=-4xyzendcases$
Not sure if I am doing fine
systems-of-equations
edited 41 mins ago
Cameron Buie
87.6k773162
asked 44 mins ago
DavidDavid
764
$endgroup$
add a comment |
$begingroup$
Solve for $begincasesfrac1x +frac1y+frac1z=0\frac4x +frac3y+frac2z=5\frac3x +frac2y+frac4z=-4endcases$
I turn the equations into $begincasesyz+xz+xy=0\4yz+3xz+2xy=5xyz\3yz+2xz+4xy=-4xyzendcases$
Not sure if I am doing fine
systems-of-equations
edited 41 mins ago
Cameron Buie
87.6k773162
asked 44 mins ago
DavidDavid
764
$endgroup$
add a comment |
$begingroup$
Solve for $begincasesfrac1x +frac1y+frac1z=0\frac4x +frac3y+frac2z=5\frac3x +frac2y+frac4z=-4endcases$
I turn the equations into $begincasesyz+xz+xy=0\4yz+3xz+2xy=5xyz\3yz+2xz+4xy=-4xyzendcases$
Not sure if I am doing fine
systems-of-equations
edited 41 mins ago
Cameron Buie
87.6k773162
asked 44 mins ago
DavidDavid
764
$endgroup$
Solve for $begincasesfrac1x +frac1y+frac1z=0\frac4x +frac3y+frac2z=5\frac3x +frac2y+frac4z=-4endcases$
I turn the equations into $begincasesyz+xz+xy=0\4yz+3xz+2xy=5xyz\3yz+2xz+4xy=-4xyzendcases$
Not sure if I am doing fine
systems-of-equations
systems-of-equations
edited 41 mins ago
Cameron Buie
87.6k773162
asked 44 mins ago
DavidDavid
764
edited 41 mins ago
Cameron Buie
87.6k773162
asked 44 mins ago
DavidDavid
764
edited 41 mins ago
Cameron Buie
87.6k773162
edited 41 mins ago
Cameron Buie
87.6k773162
edited 41 mins ago
Cameron Buie
87.6k773162
87.6k773162
asked 44 mins ago
DavidDavid
764
asked 44 mins ago
DavidDavid
764
asked 44 mins ago
DavidDavid
764
764
add a comment |
add a comment |
4 Answers
4
active
oldest
votes
$begingroup$
If the reciprocals are freaking you out, just let $t=frac1x,u=frac1y,v=frac1z,$ so you have the system $$begincasest +u+v=0\4t +3u+2v=5\3t +2u+4v=-4endcases$$ Once you've solved this, as long as none of $t,u,v$ is $0,$ you can simply let $x=frac1t,y=frac1u,z=frac1v.$ If one or more of $t,u,v$ is $0,$ then the system has no solution.
answered 38 mins ago
Cameron BuieCameron Buie
87.6k773162
$endgroup$
add a comment |
$begingroup$
It's much easier to solve the linear system for the reciprocals then take the reciprocal to get the result.
answered 43 mins ago
Matt SamuelMatt Samuel
39.7k63870
$endgroup$
add a comment |
$begingroup$
how about this, let:
$$X=frac1x,,Y=frac1y,,Z=frac1z$$
and it is much easier to solve the following:
$$beginpmatrix
1&1&1\
4&3&2\
3&2&4
endpmatrix
beginpmatrix
X\
Y\
Z
endpmatrix=
beginpmatrix
0\5\-4
endpmatrix
$$
answered 37 mins ago
Henry LeeHenry Lee
2,221319
$endgroup$
add a comment |
$begingroup$
Observe that the system's matrix of the reciprocal of the unknowns is:
$$A=beginpmatrix1&1&1&0\
4&3&2&5\
3&2&4&-4endpmatrixstackrelR_2-4R_1,,R_3-3R_1longrightarrowbeginpmatrix1&1&1&0\
0&-1&-2&5\
0&-1&-1&-4endpmatrixstackrelR_3-R_2longrightarrow$$
$$beginpmatrix1&1&1&0\
0&-1&-2&5\
0&0&1&-9endpmatrix$$
Try to finish the exercise now, taking into account that the third column represents $;cfrac 1z;$ , the second $;cfrac1y;$ and the first one $;cfrac1x;$
answered 37 mins ago
DonAntonioDonAntonio
180k1495234
$endgroup$
$begingroup$
There's an error at the 1st step: the third row should be $;0;-1; colorred+1;-4$.
$endgroup$
– Bernard
31 mins ago
add a comment |
Your Answer
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3205742%2fsolving-a-linear-system-of-reciprocals%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
4 Answers
4
active
oldest
votes
4 Answers
4
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
If the reciprocals are freaking you out, just let $t=frac1x,u=frac1y,v=frac1z,$ so you have the system $$begincasest +u+v=0\4t +3u+2v=5\3t +2u+4v=-4endcases$$ Once you've solved this, as long as none of $t,u,v$ is $0,$ you can simply let $x=frac1t,y=frac1u,z=frac1v.$ If one or more of $t,u,v$ is $0,$ then the system has no solution.
answered 38 mins ago
Cameron BuieCameron Buie
87.6k773162
$endgroup$
add a comment |
$begingroup$
If the reciprocals are freaking you out, just let $t=frac1x,u=frac1y,v=frac1z,$ so you have the system $$begincasest +u+v=0\4t +3u+2v=5\3t +2u+4v=-4endcases$$ Once you've solved this, as long as none of $t,u,v$ is $0,$ you can simply let $x=frac1t,y=frac1u,z=frac1v.$ If one or more of $t,u,v$ is $0,$ then the system has no solution.
answered 38 mins ago
Cameron BuieCameron Buie
87.6k773162
$endgroup$
add a comment |
$begingroup$
If the reciprocals are freaking you out, just let $t=frac1x,u=frac1y,v=frac1z,$ so you have the system $$begincasest +u+v=0\4t +3u+2v=5\3t +2u+4v=-4endcases$$ Once you've solved this, as long as none of $t,u,v$ is $0,$ you can simply let $x=frac1t,y=frac1u,z=frac1v.$ If one or more of $t,u,v$ is $0,$ then the system has no solution.
answered 38 mins ago
Cameron BuieCameron Buie
87.6k773162
$endgroup$
If the reciprocals are freaking you out, just let $t=frac1x,u=frac1y,v=frac1z,$ so you have the system $$begincasest +u+v=0\4t +3u+2v=5\3t +2u+4v=-4endcases$$ Once you've solved this, as long as none of $t,u,v$ is $0,$ you can simply let $x=frac1t,y=frac1u,z=frac1v.$ If one or more of $t,u,v$ is $0,$ then the system has no solution.
answered 38 mins ago
Cameron BuieCameron Buie
87.6k773162
answered 38 mins ago
Cameron BuieCameron Buie
87.6k773162
answered 38 mins ago
Cameron BuieCameron Buie
87.6k773162
answered 38 mins ago
Cameron BuieCameron Buie
87.6k773162
87.6k773162
add a comment |
add a comment |
$begingroup$
It's much easier to solve the linear system for the reciprocals then take the reciprocal to get the result.
answered 43 mins ago
Matt SamuelMatt Samuel
39.7k63870
$endgroup$
add a comment |
$begingroup$
It's much easier to solve the linear system for the reciprocals then take the reciprocal to get the result.
answered 43 mins ago
Matt SamuelMatt Samuel
39.7k63870
$endgroup$
add a comment |
$begingroup$
It's much easier to solve the linear system for the reciprocals then take the reciprocal to get the result.
answered 43 mins ago
Matt SamuelMatt Samuel
39.7k63870
$endgroup$
It's much easier to solve the linear system for the reciprocals then take the reciprocal to get the result.
answered 43 mins ago
Matt SamuelMatt Samuel
39.7k63870
answered 43 mins ago
Matt SamuelMatt Samuel
39.7k63870
answered 43 mins ago
Matt SamuelMatt Samuel
39.7k63870
answered 43 mins ago
Matt SamuelMatt Samuel
39.7k63870
39.7k63870
add a comment |
add a comment |
$begingroup$
how about this, let:
$$X=frac1x,,Y=frac1y,,Z=frac1z$$
and it is much easier to solve the following:
$$beginpmatrix
1&1&1\
4&3&2\
3&2&4
endpmatrix
beginpmatrix
X\
Y\
Z
endpmatrix=
beginpmatrix
0\5\-4
endpmatrix
$$
answered 37 mins ago
Henry LeeHenry Lee
2,221319
$endgroup$
add a comment |
$begingroup$
how about this, let:
$$X=frac1x,,Y=frac1y,,Z=frac1z$$
and it is much easier to solve the following:
$$beginpmatrix
1&1&1\
4&3&2\
3&2&4
endpmatrix
beginpmatrix
X\
Y\
Z
endpmatrix=
beginpmatrix
0\5\-4
endpmatrix
$$
answered 37 mins ago
Henry LeeHenry Lee
2,221319
$endgroup$
add a comment |
$begingroup$
how about this, let:
$$X=frac1x,,Y=frac1y,,Z=frac1z$$
and it is much easier to solve the following:
$$beginpmatrix
1&1&1\
4&3&2\
3&2&4
endpmatrix
beginpmatrix
X\
Y\
Z
endpmatrix=
beginpmatrix
0\5\-4
endpmatrix
$$
answered 37 mins ago
Henry LeeHenry Lee
2,221319
$endgroup$
how about this, let:
$$X=frac1x,,Y=frac1y,,Z=frac1z$$
and it is much easier to solve the following:
$$beginpmatrix
1&1&1\
4&3&2\
3&2&4
endpmatrix
beginpmatrix
X\
Y\
Z
endpmatrix=
beginpmatrix
0\5\-4
endpmatrix
$$
answered 37 mins ago
Henry LeeHenry Lee
2,221319
answered 37 mins ago
Henry LeeHenry Lee
2,221319
answered 37 mins ago
Henry LeeHenry Lee
2,221319
answered 37 mins ago
Henry LeeHenry Lee
2,221319
2,221319
add a comment |
add a comment |
$begingroup$
Observe that the system's matrix of the reciprocal of the unknowns is:
$$A=beginpmatrix1&1&1&0\
4&3&2&5\
3&2&4&-4endpmatrixstackrelR_2-4R_1,,R_3-3R_1longrightarrowbeginpmatrix1&1&1&0\
0&-1&-2&5\
0&-1&-1&-4endpmatrixstackrelR_3-R_2longrightarrow$$
$$beginpmatrix1&1&1&0\
0&-1&-2&5\
0&0&1&-9endpmatrix$$
Try to finish the exercise now, taking into account that the third column represents $;cfrac 1z;$ , the second $;cfrac1y;$ and the first one $;cfrac1x;$
answered 37 mins ago
DonAntonioDonAntonio
180k1495234
$endgroup$
$begingroup$
There's an error at the 1st step: the third row should be $;0;-1; colorred+1;-4$.
$endgroup$
– Bernard
31 mins ago
add a comment |
$begingroup$
Observe that the system's matrix of the reciprocal of the unknowns is:
$$A=beginpmatrix1&1&1&0\
4&3&2&5\
3&2&4&-4endpmatrixstackrelR_2-4R_1,,R_3-3R_1longrightarrowbeginpmatrix1&1&1&0\
0&-1&-2&5\
0&-1&-1&-4endpmatrixstackrelR_3-R_2longrightarrow$$
$$beginpmatrix1&1&1&0\
0&-1&-2&5\
0&0&1&-9endpmatrix$$
Try to finish the exercise now, taking into account that the third column represents $;cfrac 1z;$ , the second $;cfrac1y;$ and the first one $;cfrac1x;$
answered 37 mins ago
DonAntonioDonAntonio
180k1495234
$endgroup$
$begingroup$
There's an error at the 1st step: the third row should be $;0;-1; colorred+1;-4$.
$endgroup$
– Bernard
31 mins ago
add a comment |
$begingroup$
Observe that the system's matrix of the reciprocal of the unknowns is:
$$A=beginpmatrix1&1&1&0\
4&3&2&5\
3&2&4&-4endpmatrixstackrelR_2-4R_1,,R_3-3R_1longrightarrowbeginpmatrix1&1&1&0\
0&-1&-2&5\
0&-1&-1&-4endpmatrixstackrelR_3-R_2longrightarrow$$
$$beginpmatrix1&1&1&0\
0&-1&-2&5\
0&0&1&-9endpmatrix$$
Try to finish the exercise now, taking into account that the third column represents $;cfrac 1z;$ , the second $;cfrac1y;$ and the first one $;cfrac1x;$
answered 37 mins ago
DonAntonioDonAntonio
180k1495234
$endgroup$
Observe that the system's matrix of the reciprocal of the unknowns is:
$$A=beginpmatrix1&1&1&0\
4&3&2&5\
3&2&4&-4endpmatrixstackrelR_2-4R_1,,R_3-3R_1longrightarrowbeginpmatrix1&1&1&0\
0&-1&-2&5\
0&-1&-1&-4endpmatrixstackrelR_3-R_2longrightarrow$$
$$beginpmatrix1&1&1&0\
0&-1&-2&5\
0&0&1&-9endpmatrix$$
Try to finish the exercise now, taking into account that the third column represents $;cfrac 1z;$ , the second $;cfrac1y;$ and the first one $;cfrac1x;$
answered 37 mins ago
DonAntonioDonAntonio
180k1495234
answered 37 mins ago
DonAntonioDonAntonio
180k1495234
answered 37 mins ago
DonAntonioDonAntonio
180k1495234
answered 37 mins ago
DonAntonioDonAntonio
180k1495234
180k1495234
$begingroup$
There's an error at the 1st step: the third row should be $;0;-1; colorred+1;-4$.
$endgroup$
– Bernard
31 mins ago
add a comment |
$begingroup$
There's an error at the 1st step: the third row should be $;0;-1; colorred+1;-4$.
$endgroup$
– Bernard
31 mins ago
$begingroup$
There's an error at the 1st step: the third row should be $;0;-1; colorred+1;-4$.
$endgroup$
– Bernard
31 mins ago
$begingroup$
There's an error at the 1st step: the third row should be $;0;-1; colorred+1;-4$.
$endgroup$
– Bernard
31 mins ago
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3205742%2fsolving-a-linear-system-of-reciprocals%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
