Rank of a matrix based on its pivot elements
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In the example given in this Wikipedia article, I wonder if the last step is necessary to get its row echelon form. Why is it done? We have an upper triangular matrix in the previous step and we can then see its rank is equal to its non-zero rows which is two.
My other question is, what does it mean when it says the rank is the number of pivots (which is means the number of columns?)? There are three columns in the above example but the rank is not three. Any clarifications would be greatly appreciated.
Here's the image for your convenience:
linear-algebra
asked Jan 7 '14 at 11:18
GigiliGigili
3,38042555
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add a comment |
$begingroup$
In the example given in this Wikipedia article, I wonder if the last step is necessary to get its row echelon form. Why is it done? We have an upper triangular matrix in the previous step and we can then see its rank is equal to its non-zero rows which is two.
My other question is, what does it mean when it says the rank is the number of pivots (which is means the number of columns?)? There are three columns in the above example but the rank is not three. Any clarifications would be greatly appreciated.
Here's the image for your convenience:
linear-algebra
asked Jan 7 '14 at 11:18
GigiliGigili
3,38042555
$endgroup$
add a comment |
$begingroup$
In the example given in this Wikipedia article, I wonder if the last step is necessary to get its row echelon form. Why is it done? We have an upper triangular matrix in the previous step and we can then see its rank is equal to its non-zero rows which is two.
My other question is, what does it mean when it says the rank is the number of pivots (which is means the number of columns?)? There are three columns in the above example but the rank is not three. Any clarifications would be greatly appreciated.
Here's the image for your convenience:
linear-algebra
asked Jan 7 '14 at 11:18
GigiliGigili
3,38042555
$endgroup$
In the example given in this Wikipedia article, I wonder if the last step is necessary to get its row echelon form. Why is it done? We have an upper triangular matrix in the previous step and we can then see its rank is equal to its non-zero rows which is two.
My other question is, what does it mean when it says the rank is the number of pivots (which is means the number of columns?)? There are three columns in the above example but the rank is not three. Any clarifications would be greatly appreciated.
Here's the image for your convenience:
linear-algebra
linear-algebra
asked Jan 7 '14 at 11:18
GigiliGigili
3,38042555
asked Jan 7 '14 at 11:18
GigiliGigili
3,38042555
edited Jan 7 '14 at 12:00
Gigili
asked Jan 7 '14 at 11:18
GigiliGigili
3,38042555
asked Jan 7 '14 at 11:18
GigiliGigili
3,38042555
asked Jan 7 '14 at 11:18
GigiliGigili
3,38042555
3,38042555
add a comment |
add a comment |
1 Answer
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number of pivot elements indicate number of independent rows or columns in given matrix ,which is on the other hand ,exactly rank of matrix,in your case we have two leading $1$,it means that rank is equal to $2$
answered Jan 7 '14 at 11:21
dato datuashvilidato datuashvili
5,4991354107
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Thank you for your answer. Which columns are you referring to as independent? And could you answer my other question too?
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– Gigili
Jan 7 '14 at 11:23
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now i have not time sorry,which columns are independent or basis?in your case first and second,because in these two column after row echelon form,you have two leading one,leading 1 should be from previous one right and below,no on the same row
$endgroup$
– dato datuashvili
Jan 7 '14 at 11:24
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any question please?
$endgroup$
– dato datuashvili
Jan 7 '14 at 11:36
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I thought you had no time
$endgroup$
– Gigili
Jan 7 '14 at 11:40
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i meant to answer related to your other question posted there,but related to this one i meant
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– dato datuashvili
Jan 7 '14 at 11:41
add a comment |
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$begingroup$
number of pivot elements indicate number of independent rows or columns in given matrix ,which is on the other hand ,exactly rank of matrix,in your case we have two leading $1$,it means that rank is equal to $2$
answered Jan 7 '14 at 11:21
dato datuashvilidato datuashvili
5,4991354107
$endgroup$
$begingroup$
Thank you for your answer. Which columns are you referring to as independent? And could you answer my other question too?
$endgroup$
– Gigili
Jan 7 '14 at 11:23
$begingroup$
now i have not time sorry,which columns are independent or basis?in your case first and second,because in these two column after row echelon form,you have two leading one,leading 1 should be from previous one right and below,no on the same row
$endgroup$
– dato datuashvili
Jan 7 '14 at 11:24
$begingroup$
any question please?
$endgroup$
– dato datuashvili
Jan 7 '14 at 11:36
$begingroup$
I thought you had no time
$endgroup$
– Gigili
Jan 7 '14 at 11:40
$begingroup$
i meant to answer related to your other question posted there,but related to this one i meant
$endgroup$
– dato datuashvili
Jan 7 '14 at 11:41
add a comment |
$begingroup$
number of pivot elements indicate number of independent rows or columns in given matrix ,which is on the other hand ,exactly rank of matrix,in your case we have two leading $1$,it means that rank is equal to $2$
answered Jan 7 '14 at 11:21
dato datuashvilidato datuashvili
5,4991354107
$endgroup$
$begingroup$
Thank you for your answer. Which columns are you referring to as independent? And could you answer my other question too?
$endgroup$
– Gigili
Jan 7 '14 at 11:23
$begingroup$
now i have not time sorry,which columns are independent or basis?in your case first and second,because in these two column after row echelon form,you have two leading one,leading 1 should be from previous one right and below,no on the same row
$endgroup$
– dato datuashvili
Jan 7 '14 at 11:24
$begingroup$
any question please?
$endgroup$
– dato datuashvili
Jan 7 '14 at 11:36
$begingroup$
I thought you had no time
$endgroup$
– Gigili
Jan 7 '14 at 11:40
$begingroup$
i meant to answer related to your other question posted there,but related to this one i meant
$endgroup$
– dato datuashvili
Jan 7 '14 at 11:41
add a comment |
$begingroup$
number of pivot elements indicate number of independent rows or columns in given matrix ,which is on the other hand ,exactly rank of matrix,in your case we have two leading $1$,it means that rank is equal to $2$
answered Jan 7 '14 at 11:21
dato datuashvilidato datuashvili
5,4991354107
$endgroup$
number of pivot elements indicate number of independent rows or columns in given matrix ,which is on the other hand ,exactly rank of matrix,in your case we have two leading $1$,it means that rank is equal to $2$
answered Jan 7 '14 at 11:21
dato datuashvilidato datuashvili
5,4991354107
answered Jan 7 '14 at 11:21
dato datuashvilidato datuashvili
5,4991354107
answered Jan 7 '14 at 11:21
dato datuashvilidato datuashvili
5,4991354107
answered Jan 7 '14 at 11:21
dato datuashvilidato datuashvili
5,4991354107
5,4991354107
$begingroup$
Thank you for your answer. Which columns are you referring to as independent? And could you answer my other question too?
$endgroup$
– Gigili
Jan 7 '14 at 11:23
$begingroup$
now i have not time sorry,which columns are independent or basis?in your case first and second,because in these two column after row echelon form,you have two leading one,leading 1 should be from previous one right and below,no on the same row
$endgroup$
– dato datuashvili
Jan 7 '14 at 11:24
$begingroup$
any question please?
$endgroup$
– dato datuashvili
Jan 7 '14 at 11:36
$begingroup$
I thought you had no time
$endgroup$
– Gigili
Jan 7 '14 at 11:40
$begingroup$
i meant to answer related to your other question posted there,but related to this one i meant
$endgroup$
– dato datuashvili
Jan 7 '14 at 11:41
add a comment |
$begingroup$
Thank you for your answer. Which columns are you referring to as independent? And could you answer my other question too?
$endgroup$
– Gigili
Jan 7 '14 at 11:23
$begingroup$
now i have not time sorry,which columns are independent or basis?in your case first and second,because in these two column after row echelon form,you have two leading one,leading 1 should be from previous one right and below,no on the same row
$endgroup$
– dato datuashvili
Jan 7 '14 at 11:24
$begingroup$
any question please?
$endgroup$
– dato datuashvili
Jan 7 '14 at 11:36
$begingroup$
I thought you had no time
$endgroup$
– Gigili
Jan 7 '14 at 11:40
$begingroup$
i meant to answer related to your other question posted there,but related to this one i meant
$endgroup$
– dato datuashvili
Jan 7 '14 at 11:41
$begingroup$
Thank you for your answer. Which columns are you referring to as independent? And could you answer my other question too?
$endgroup$
– Gigili
Jan 7 '14 at 11:23
$begingroup$
Thank you for your answer. Which columns are you referring to as independent? And could you answer my other question too?
$endgroup$
– Gigili
Jan 7 '14 at 11:23
$begingroup$
now i have not time sorry,which columns are independent or basis?in your case first and second,because in these two column after row echelon form,you have two leading one,leading 1 should be from previous one right and below,no on the same row
$endgroup$
– dato datuashvili
Jan 7 '14 at 11:24
$begingroup$
now i have not time sorry,which columns are independent or basis?in your case first and second,because in these two column after row echelon form,you have two leading one,leading 1 should be from previous one right and below,no on the same row
$endgroup$
– dato datuashvili
Jan 7 '14 at 11:24
$begingroup$
any question please?
$endgroup$
– dato datuashvili
Jan 7 '14 at 11:36
$begingroup$
any question please?
$endgroup$
– dato datuashvili
Jan 7 '14 at 11:36
$begingroup$
I thought you had no time
$endgroup$
– Gigili
Jan 7 '14 at 11:40
$begingroup$
I thought you had no time
$endgroup$
– Gigili
Jan 7 '14 at 11:40
$begingroup$
i meant to answer related to your other question posted there,but related to this one i meant
$endgroup$
– dato datuashvili
Jan 7 '14 at 11:41
$begingroup$
i meant to answer related to your other question posted there,but related to this one i meant
$endgroup$
– dato datuashvili
Jan 7 '14 at 11:41
add a comment |
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