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April 9th, 2010, 02:59 PM   #1
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Computing the rank of this matrix quickly?

How do I quickly find the rank of this matrix?

A =

element and subtracting from each of the rows i > 1 a multiple of row 1 that gives 0 in the first column for each row after i >1 we have that

for i > 2. This gives similar matrix A'

A' =

Divide each of these elements by -5(i-1) = 5(1- i) (which you can do because you're dividing each element of the same row by the same number) and you get that (for each row after row 1) the elements are just j-1 , row 2,3,4, and 5 become [0 1 2 3 4]. So the last 3 rows are redundant, and thus the rank is 2. That is A' becomes similar matrix A'':

A'' =
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April 10th, 2010, 11:39 PM   #2
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Re: Computing the rank of this matrix quickly?

You can take the line and substract the line for from to .
You will obtain :
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April 12th, 2010, 02:39 PM   #3
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Re: Computing the rank of this matrix quickly?

Oh, nicely done.
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April 16th, 2010, 12:30 PM   #4
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Re: Computing the rank of this matrix quickly?

smart
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