Mixing
find vector equation of a hyperplane in $mathbb R^4$ from scalar equation
$begingroup$
How would I go about finding a vector equation of a hyperplane $$3x_1+x_2-2x_3+4x_4=5$$
I know I need to find 3 vectors and another vector that shifts from the origin in the form
$$rvec{a}+svec{b}+tvec{c}+vec{d}$$
linear-algebra vectors
edited Jan 28 at 20:32
J. W. Tanner
4,0461320
asked Jan 28 at 19:34
Jerry W.Jerry W.
535
$endgroup$
add a comment |
$begingroup$
How would I go about finding a vector equation of a hyperplane $$3x_1+x_2-2x_3+4x_4=5$$
I know I need to find 3 vectors and another vector that shifts from the origin in the form
$$rvec{a}+svec{b}+tvec{c}+vec{d}$$
linear-algebra vectors
edited Jan 28 at 20:32
J. W. Tanner
4,0461320
asked Jan 28 at 19:34
Jerry W.Jerry W.
535
$endgroup$
add a comment |
$begingroup$
How would I go about finding a vector equation of a hyperplane $$3x_1+x_2-2x_3+4x_4=5$$
I know I need to find 3 vectors and another vector that shifts from the origin in the form
$$rvec{a}+svec{b}+tvec{c}+vec{d}$$
linear-algebra vectors
edited Jan 28 at 20:32
J. W. Tanner
4,0461320
asked Jan 28 at 19:34
Jerry W.Jerry W.
535
$endgroup$
How would I go about finding a vector equation of a hyperplane $$3x_1+x_2-2x_3+4x_4=5$$
I know I need to find 3 vectors and another vector that shifts from the origin in the form
$$rvec{a}+svec{b}+tvec{c}+vec{d}$$
linear-algebra vectors
linear-algebra vectors
edited Jan 28 at 20:32
J. W. Tanner
4,0461320
asked Jan 28 at 19:34
Jerry W.Jerry W.
535
edited Jan 28 at 20:32
J. W. Tanner
4,0461320
asked Jan 28 at 19:34
Jerry W.Jerry W.
535
edited Jan 28 at 20:32
J. W. Tanner
4,0461320
edited Jan 28 at 20:32
J. W. Tanner
4,0461320
edited Jan 28 at 20:32
J. W. Tanner
4,0461320
4,0461320
asked Jan 28 at 19:34
Jerry W.Jerry W.
535
asked Jan 28 at 19:34
Jerry W.Jerry W.
535
asked Jan 28 at 19:34
Jerry W.Jerry W.
535
535
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Hint: Take $x_1,x_3,x_4$ to be free variables. Then,
$$x_1=x_1$$
$$x_2=5-3x_1+2x_3-4x_4$$
$$x_3=x_3$$
$$x_4=x_4$$
Now write this in vector notation.
answered Jan 28 at 19:39
Ahmed S. AttaallaAhmed S. Attaalla
14.9k12151
$endgroup$
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%2f3091295%2ffind-vector-equation-of-a-hyperplane-in-mathbb-r4-from-scalar-equation%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Hint: Take $x_1,x_3,x_4$ to be free variables. Then,
$$x_1=x_1$$
$$x_2=5-3x_1+2x_3-4x_4$$
$$x_3=x_3$$
$$x_4=x_4$$
Now write this in vector notation.
answered Jan 28 at 19:39
Ahmed S. AttaallaAhmed S. Attaalla
14.9k12151
$endgroup$
add a comment |
$begingroup$
Hint: Take $x_1,x_3,x_4$ to be free variables. Then,
$$x_1=x_1$$
$$x_2=5-3x_1+2x_3-4x_4$$
$$x_3=x_3$$
$$x_4=x_4$$
Now write this in vector notation.
answered Jan 28 at 19:39
Ahmed S. AttaallaAhmed S. Attaalla
14.9k12151
$endgroup$
add a comment |
$begingroup$
Hint: Take $x_1,x_3,x_4$ to be free variables. Then,
$$x_1=x_1$$
$$x_2=5-3x_1+2x_3-4x_4$$
$$x_3=x_3$$
$$x_4=x_4$$
Now write this in vector notation.
answered Jan 28 at 19:39
Ahmed S. AttaallaAhmed S. Attaalla
14.9k12151
$endgroup$
Hint: Take $x_1,x_3,x_4$ to be free variables. Then,
$$x_1=x_1$$
$$x_2=5-3x_1+2x_3-4x_4$$
$$x_3=x_3$$
$$x_4=x_4$$
Now write this in vector notation.
answered Jan 28 at 19:39
Ahmed S. AttaallaAhmed S. Attaalla
14.9k12151
answered Jan 28 at 19:39
Ahmed S. AttaallaAhmed S. Attaalla
14.9k12151
answered Jan 28 at 19:39
Ahmed S. AttaallaAhmed S. Attaalla
14.9k12151
answered Jan 28 at 19:39
Ahmed S. AttaallaAhmed S. Attaalla
14.9k12151
14.9k12151
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%2f3091295%2ffind-vector-equation-of-a-hyperplane-in-mathbb-r4-from-scalar-equation%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
