Linear Independence of given vectors
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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
41k137198
asked Nov 17 at 23:33
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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
41k137198
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
41k137198
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
41k137198
asked Nov 17 at 23:33
contttttt
11
edited Nov 18 at 2:56
Parcly Taxel
41k137198
asked Nov 17 at 23:33
contttttt
11
edited Nov 18 at 2:56
Parcly Taxel
41k137198
edited Nov 18 at 2:56
Parcly Taxel
41k137198
edited Nov 18 at 2:56
Parcly Taxel
41k137198
41k137198
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 |
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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