Linear Independence of given vectors
up vote
0
down vote
favorite
Find all real numbers $x$ for which the vectors $m_1=(1,1,x,0)$, $m_2=(1,-x,x-1,3)$, $m_3=(0,-2,1,x)$, $m_4=(1,-3,-1,2x)$ are linearly dependent. For these values of $x$, explain how you know that the vectors are linearly independent for all other values of $x$.
I have found the values of $x$ but am struggling with what to write for the part about how I know for all other values of $x$ the vectors are linearly independent, is it related to the fact I found these values of $x$ using Gaussian elimination and how it will only give values of $x$ for which the vectors are linearly dependent?
vectors
edited Nov 18 at 2:56
Parcly Taxel
41k137199
asked Nov 17 at 23:33
contttttt
11
add a comment |
up vote
0
down vote
favorite
Find all real numbers $x$ for which the vectors $m_1=(1,1,x,0)$, $m_2=(1,-x,x-1,3)$, $m_3=(0,-2,1,x)$, $m_4=(1,-3,-1,2x)$ are linearly dependent. For these values of $x$, explain how you know that the vectors are linearly independent for all other values of $x$.
I have found the values of $x$ but am struggling with what to write for the part about how I know for all other values of $x$ the vectors are linearly independent, is it related to the fact I found these values of $x$ using Gaussian elimination and how it will only give values of $x$ for which the vectors are linearly dependent?
vectors
edited Nov 18 at 2:56
Parcly Taxel
41k137199
asked Nov 17 at 23:33
contttttt
11
Form a matrix by using it. Then reduce it and determine its determinant. If det. is $0$ then Linearly dependent otherwise linearly independent. Now you can check what is the role of $x$?
– John Nash
Nov 17 at 23:53
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Find all real numbers $x$ for which the vectors $m_1=(1,1,x,0)$, $m_2=(1,-x,x-1,3)$, $m_3=(0,-2,1,x)$, $m_4=(1,-3,-1,2x)$ are linearly dependent. For these values of $x$, explain how you know that the vectors are linearly independent for all other values of $x$.
I have found the values of $x$ but am struggling with what to write for the part about how I know for all other values of $x$ the vectors are linearly independent, is it related to the fact I found these values of $x$ using Gaussian elimination and how it will only give values of $x$ for which the vectors are linearly dependent?
vectors
edited Nov 18 at 2:56
Parcly Taxel
41k137199
asked Nov 17 at 23:33
contttttt
11
Find all real numbers $x$ for which the vectors $m_1=(1,1,x,0)$, $m_2=(1,-x,x-1,3)$, $m_3=(0,-2,1,x)$, $m_4=(1,-3,-1,2x)$ are linearly dependent. For these values of $x$, explain how you know that the vectors are linearly independent for all other values of $x$.
I have found the values of $x$ but am struggling with what to write for the part about how I know for all other values of $x$ the vectors are linearly independent, is it related to the fact I found these values of $x$ using Gaussian elimination and how it will only give values of $x$ for which the vectors are linearly dependent?
vectors
vectors
edited Nov 18 at 2:56
Parcly Taxel
41k137199
asked Nov 17 at 23:33
contttttt
11
edited Nov 18 at 2:56
Parcly Taxel
41k137199
asked Nov 17 at 23:33
contttttt
11
edited Nov 18 at 2:56
Parcly Taxel
41k137199
edited Nov 18 at 2:56
Parcly Taxel
41k137199
edited Nov 18 at 2:56
Parcly Taxel
41k137199
41k137199
asked Nov 17 at 23:33
contttttt
11
asked Nov 17 at 23:33
contttttt
11
asked Nov 17 at 23:33
contttttt
11
11
Form a matrix by using it. Then reduce it and determine its determinant. If det. is $0$ then Linearly dependent otherwise linearly independent. Now you can check what is the role of $x$?
– John Nash
Nov 17 at 23:53
add a comment |
Form a matrix by using it. Then reduce it and determine its determinant. If det. is $0$ then Linearly dependent otherwise linearly independent. Now you can check what is the role of $x$?
– John Nash
Nov 17 at 23:53
Form a matrix by using it. Then reduce it and determine its determinant. If det. is $0$ then Linearly dependent otherwise linearly independent. Now you can check what is the role of $x$?
– John Nash
Nov 17 at 23:53
Form a matrix by using it. Then reduce it and determine its determinant. If det. is $0$ then Linearly dependent otherwise linearly independent. Now you can check what is the role of $x$?
– John Nash
Nov 17 at 23:53
add a comment |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
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%2f3002950%2flinear-independence-of-given-vectors%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
Form a matrix by using it. Then reduce it and determine its determinant. If det. is $0$ then Linearly dependent otherwise linearly independent. Now you can check what is the role of $x$?
– John Nash
Nov 17 at 23:53