Solve $x = Cx+d$ for $x$Solving matrix equations of the form $X = AXA^T + C$Transition matrix homeworkFractional power of matrixProbability Markov chain, system of equationsSolve $Ux=y$ for $x$How to subselect columns of a matrix?System of linear equations - ResolutionInverse of a matrix whose elements are arraysConverging matrix and its formDot Product, matrix multiplication etc
is this saw blade faulty?
Is VPN a layer 3 concept?
Homology of the fiber
How do you justify more code being written by following clean code practices?
Why is participating in the European Parliamentary elections used as a threat?
Is a square zero matrix positive semidefinite?
PTIJ: Which Dr. Seuss books should one obtain?
Why do I have a large white artefact on the rendered image?
Would this string work as string?
"Marked down as someone wanting to sell shares." What does that mean?
Unfrosted light bulb
The English Debate
Have the tides ever turned twice on any open problem?
Do native speakers use "ultima" and "proxima" frequently in spoken English?
Animating wave motion in water
Have any astronauts/cosmonauts died in space?
Why I don't get the wanted width of tcbox?
Hackerrank All Women's Codesprint 2019: Name the Product
How much propellant is used up until liftoff?
Determine voltage drop over 10G resistors with cheap multimeter
How can I create URL shortcuts/redirects for task/diff IDs in Phabricator?
pipe commands inside find -exec?
Why doesn't the fusion process of the sun speed up?
Exposing a company lying about themselves in a tightly knit industry: Is my career at risk on the long run?
Solve $x = Cx+d$ for $x$
Solving matrix equations of the form $X = AXA^T + C$Transition matrix homeworkFractional power of matrixProbability Markov chain, system of equationsSolve $Ux=y$ for $x$How to subselect columns of a matrix?System of linear equations - ResolutionInverse of a matrix whose elements are arraysConverging matrix and its formDot Product, matrix multiplication etc
$begingroup$
Given
$$C = beginbmatrix
0.7 & 0.2 \
0.1 & 0.5 \
endbmatrix qquad text and qquad
d = beginbmatrix
26\
52\
endbmatrix$$
Solve the equation $x = C x + d$ for $x$.
I'm a little confused as to why $x$ is on both sides of the equation. Am I supposed to find the determinant to solve this?
Update: I multiplied the identity matrix by matrix $C$. Then I multiplied this times $d$ to get $x$. Which gave me the answer:
beginbmatrix
180\
140\
endbmatrix
linear-algebra matrices systems-of-equations
edited Mar 13 at 11:58
Rodrigo de Azevedo
13.1k41960
asked Mar 13 at 7:37
K JayK Jay
316
$endgroup$
add a comment |
$begingroup$
Given
$$C = beginbmatrix
0.7 & 0.2 \
0.1 & 0.5 \
endbmatrix qquad text and qquad
d = beginbmatrix
26\
52\
endbmatrix$$
Solve the equation $x = C x + d$ for $x$.
I'm a little confused as to why $x$ is on both sides of the equation. Am I supposed to find the determinant to solve this?
Update: I multiplied the identity matrix by matrix $C$. Then I multiplied this times $d$ to get $x$. Which gave me the answer:
beginbmatrix
180\
140\
endbmatrix
linear-algebra matrices systems-of-equations
edited Mar 13 at 11:58
Rodrigo de Azevedo
13.1k41960
asked Mar 13 at 7:37
K JayK Jay
316
$endgroup$
7
$begingroup$
Idea: Write your equation as $$(I-C)x=d$$ and then solve for $x$ as usual!
$endgroup$
– Chinnapparaj R
Mar 13 at 7:40
$begingroup$
So $$beginalign & beginbmatrix 1 & 0\ 0 & 1\ endbmatrixx - beginbmatrix 0.7 & 0.2 \ 0.1 & 0.5 \ endbmatrix x & = beginbmatrix 26\ 52\ endbmatrixendalign$$ ?
$endgroup$
– K Jay
Mar 13 at 8:05
1
$begingroup$
Yes! $$beginpmatrix 0.3&0.2\0.1&0.5 endpmatrix beginpmatrix a\b endpmatrix =beginpmatrix 26\52 endpmatrix$$ and then find $a$ and $b$
$endgroup$
– Chinnapparaj R
Mar 13 at 8:09
$begingroup$
sorry, $a_12=-0.2$ and $a_21=-0.1$
$endgroup$
– Chinnapparaj R
Mar 13 at 8:17
$begingroup$
So then how do I solve for $$ a text and b$$. Do I find the inverse of C and multiply that times d?
$endgroup$
– K Jay
Mar 13 at 8:21
add a comment |
$begingroup$
Given
$$C = beginbmatrix
0.7 & 0.2 \
0.1 & 0.5 \
endbmatrix qquad text and qquad
d = beginbmatrix
26\
52\
endbmatrix$$
Solve the equation $x = C x + d$ for $x$.
I'm a little confused as to why $x$ is on both sides of the equation. Am I supposed to find the determinant to solve this?
Update: I multiplied the identity matrix by matrix $C$. Then I multiplied this times $d$ to get $x$. Which gave me the answer:
beginbmatrix
180\
140\
endbmatrix
linear-algebra matrices systems-of-equations
edited Mar 13 at 11:58
Rodrigo de Azevedo
13.1k41960
asked Mar 13 at 7:37
K JayK Jay
316
$endgroup$
Given
$$C = beginbmatrix
0.7 & 0.2 \
0.1 & 0.5 \
endbmatrix qquad text and qquad
d = beginbmatrix
26\
52\
endbmatrix$$
Solve the equation $x = C x + d$ for $x$.
I'm a little confused as to why $x$ is on both sides of the equation. Am I supposed to find the determinant to solve this?
Update: I multiplied the identity matrix by matrix $C$. Then I multiplied this times $d$ to get $x$. Which gave me the answer:
beginbmatrix
180\
140\
endbmatrix
linear-algebra matrices systems-of-equations
linear-algebra matrices systems-of-equations
edited Mar 13 at 11:58
Rodrigo de Azevedo
13.1k41960
asked Mar 13 at 7:37
K JayK Jay
316
edited Mar 13 at 11:58
Rodrigo de Azevedo
13.1k41960
asked Mar 13 at 7:37
K JayK Jay
316
edited Mar 13 at 11:58
Rodrigo de Azevedo
13.1k41960
edited Mar 13 at 11:58
Rodrigo de Azevedo
13.1k41960
edited Mar 13 at 11:58
Rodrigo de Azevedo
13.1k41960
13.1k41960
asked Mar 13 at 7:37
K JayK Jay
316
asked Mar 13 at 7:37
K JayK Jay
316
asked Mar 13 at 7:37
K JayK Jay
316
316
7
$begingroup$
Idea: Write your equation as $$(I-C)x=d$$ and then solve for $x$ as usual!
$endgroup$
– Chinnapparaj R
Mar 13 at 7:40
$begingroup$
So $$beginalign & beginbmatrix 1 & 0\ 0 & 1\ endbmatrixx - beginbmatrix 0.7 & 0.2 \ 0.1 & 0.5 \ endbmatrix x & = beginbmatrix 26\ 52\ endbmatrixendalign$$ ?
$endgroup$
– K Jay
Mar 13 at 8:05
1
$begingroup$
Yes! $$beginpmatrix 0.3&0.2\0.1&0.5 endpmatrix beginpmatrix a\b endpmatrix =beginpmatrix 26\52 endpmatrix$$ and then find $a$ and $b$
$endgroup$
– Chinnapparaj R
Mar 13 at 8:09
$begingroup$
sorry, $a_12=-0.2$ and $a_21=-0.1$
$endgroup$
– Chinnapparaj R
Mar 13 at 8:17
$begingroup$
So then how do I solve for $$ a text and b$$. Do I find the inverse of C and multiply that times d?
$endgroup$
– K Jay
Mar 13 at 8:21
add a comment |
7
$begingroup$
Idea: Write your equation as $$(I-C)x=d$$ and then solve for $x$ as usual!
$endgroup$
– Chinnapparaj R
Mar 13 at 7:40
$begingroup$
So $$beginalign & beginbmatrix 1 & 0\ 0 & 1\ endbmatrixx - beginbmatrix 0.7 & 0.2 \ 0.1 & 0.5 \ endbmatrix x & = beginbmatrix 26\ 52\ endbmatrixendalign$$ ?
$endgroup$
– K Jay
Mar 13 at 8:05
1
$begingroup$
Yes! $$beginpmatrix 0.3&0.2\0.1&0.5 endpmatrix beginpmatrix a\b endpmatrix =beginpmatrix 26\52 endpmatrix$$ and then find $a$ and $b$
$endgroup$
– Chinnapparaj R
Mar 13 at 8:09
$begingroup$
sorry, $a_12=-0.2$ and $a_21=-0.1$
$endgroup$
– Chinnapparaj R
Mar 13 at 8:17
$begingroup$
So then how do I solve for $$ a text and b$$. Do I find the inverse of C and multiply that times d?
$endgroup$
– K Jay
Mar 13 at 8:21
7
7
$begingroup$
Idea: Write your equation as $$(I-C)x=d$$ and then solve for $x$ as usual!
$endgroup$
– Chinnapparaj R
Mar 13 at 7:40
$begingroup$
Idea: Write your equation as $$(I-C)x=d$$ and then solve for $x$ as usual!
$endgroup$
– Chinnapparaj R
Mar 13 at 7:40
$begingroup$
So $$beginalign & beginbmatrix 1 & 0\ 0 & 1\ endbmatrixx - beginbmatrix 0.7 & 0.2 \ 0.1 & 0.5 \ endbmatrix x & = beginbmatrix 26\ 52\ endbmatrixendalign$$ ?
$endgroup$
– K Jay
Mar 13 at 8:05
$begingroup$
So $$beginalign & beginbmatrix 1 & 0\ 0 & 1\ endbmatrixx - beginbmatrix 0.7 & 0.2 \ 0.1 & 0.5 \ endbmatrix x & = beginbmatrix 26\ 52\ endbmatrixendalign$$ ?
$endgroup$
– K Jay
Mar 13 at 8:05
1
1
$begingroup$
Yes! $$beginpmatrix 0.3&0.2\0.1&0.5 endpmatrix beginpmatrix a\b endpmatrix =beginpmatrix 26\52 endpmatrix$$ and then find $a$ and $b$
$endgroup$
– Chinnapparaj R
Mar 13 at 8:09
$begingroup$
Yes! $$beginpmatrix 0.3&0.2\0.1&0.5 endpmatrix beginpmatrix a\b endpmatrix =beginpmatrix 26\52 endpmatrix$$ and then find $a$ and $b$
$endgroup$
– Chinnapparaj R
Mar 13 at 8:09
$begingroup$
sorry, $a_12=-0.2$ and $a_21=-0.1$
$endgroup$
– Chinnapparaj R
Mar 13 at 8:17
$begingroup$
sorry, $a_12=-0.2$ and $a_21=-0.1$
$endgroup$
– Chinnapparaj R
Mar 13 at 8:17
$begingroup$
So then how do I solve for $$ a text and b$$. Do I find the inverse of C and multiply that times d?
$endgroup$
– K Jay
Mar 13 at 8:21
$begingroup$
So then how do I solve for $$ a text and b$$. Do I find the inverse of C and multiply that times d?
$endgroup$
– K Jay
Mar 13 at 8:21
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Hint
Substitute $x=Ix=beginbmatrix1&0\0&1endbmatrixx$ and solve $$(C-I)x+d=0$$
answered Mar 13 at 12:13
Mostafa AyazMostafa Ayaz
16.5k3939
$endgroup$
add a comment |
$begingroup$
With $x=(u,v)$ the equation $x= Cx+d $ is equivalent to
$u=0.7u+0.2v+26$
$v=0.1u+0.5v+52.$
Can you take it from here?
answered Mar 13 at 7:52
FredFred
48.5k1849
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");
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%2f3146227%2fsolve-x-cxd-for-x%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Hint
Substitute $x=Ix=beginbmatrix1&0\0&1endbmatrixx$ and solve $$(C-I)x+d=0$$
answered Mar 13 at 12:13
Mostafa AyazMostafa Ayaz
16.5k3939
$endgroup$
add a comment |
$begingroup$
Hint
Substitute $x=Ix=beginbmatrix1&0\0&1endbmatrixx$ and solve $$(C-I)x+d=0$$
answered Mar 13 at 12:13
Mostafa AyazMostafa Ayaz
16.5k3939
$endgroup$
add a comment |
$begingroup$
Hint
Substitute $x=Ix=beginbmatrix1&0\0&1endbmatrixx$ and solve $$(C-I)x+d=0$$
answered Mar 13 at 12:13
Mostafa AyazMostafa Ayaz
16.5k3939
$endgroup$
Hint
Substitute $x=Ix=beginbmatrix1&0\0&1endbmatrixx$ and solve $$(C-I)x+d=0$$
answered Mar 13 at 12:13
Mostafa AyazMostafa Ayaz
16.5k3939
answered Mar 13 at 12:13
Mostafa AyazMostafa Ayaz
16.5k3939
answered Mar 13 at 12:13
Mostafa AyazMostafa Ayaz
16.5k3939
answered Mar 13 at 12:13
Mostafa AyazMostafa Ayaz
16.5k3939
16.5k3939
add a comment |
add a comment |
$begingroup$
With $x=(u,v)$ the equation $x= Cx+d $ is equivalent to
$u=0.7u+0.2v+26$
$v=0.1u+0.5v+52.$
Can you take it from here?
answered Mar 13 at 7:52
FredFred
48.5k1849
$endgroup$
add a comment |
$begingroup$
With $x=(u,v)$ the equation $x= Cx+d $ is equivalent to
$u=0.7u+0.2v+26$
$v=0.1u+0.5v+52.$
Can you take it from here?
answered Mar 13 at 7:52
FredFred
48.5k1849
$endgroup$
add a comment |
$begingroup$
With $x=(u,v)$ the equation $x= Cx+d $ is equivalent to
$u=0.7u+0.2v+26$
$v=0.1u+0.5v+52.$
Can you take it from here?
answered Mar 13 at 7:52
FredFred
48.5k1849
$endgroup$
With $x=(u,v)$ the equation $x= Cx+d $ is equivalent to
$u=0.7u+0.2v+26$
$v=0.1u+0.5v+52.$
Can you take it from here?
answered Mar 13 at 7:52
FredFred
48.5k1849
answered Mar 13 at 7:52
FredFred
48.5k1849
answered Mar 13 at 7:52
FredFred
48.5k1849
answered Mar 13 at 7:52
FredFred
48.5k1849
48.5k1849
add a comment |
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%2f3146227%2fsolve-x-cxd-for-x%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
7
$begingroup$
Idea: Write your equation as $$(I-C)x=d$$ and then solve for $x$ as usual!
$endgroup$
– Chinnapparaj R
Mar 13 at 7:40
$begingroup$
So $$beginalign & beginbmatrix 1 & 0\ 0 & 1\ endbmatrixx - beginbmatrix 0.7 & 0.2 \ 0.1 & 0.5 \ endbmatrix x & = beginbmatrix 26\ 52\ endbmatrixendalign$$ ?
$endgroup$
– K Jay
Mar 13 at 8:05
1
$begingroup$
Yes! $$beginpmatrix 0.3&0.2\0.1&0.5 endpmatrix beginpmatrix a\b endpmatrix =beginpmatrix 26\52 endpmatrix$$ and then find $a$ and $b$
$endgroup$
– Chinnapparaj R
Mar 13 at 8:09
$begingroup$
sorry, $a_12=-0.2$ and $a_21=-0.1$
$endgroup$
– Chinnapparaj R
Mar 13 at 8:17
$begingroup$
So then how do I solve for $$ a text and b$$. Do I find the inverse of C and multiply that times d?
$endgroup$
– K Jay
Mar 13 at 8:21