bhuvaneshnick
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- Dec 18, 2014
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The maximum number of linear independent column vectors of matrix A is called rank of matrix
The maximum number of linear independent column vectors of matrix A is called rank of matrix
i have not head this line ever,What does mean independent column vector .i would be nice to understand if u say what also dependent column vectors Thank youCode:The maximum number of linear independent column vectors of matrix A is called rank of matrix
Do some google-search for "rank of matrix"
Start investigation with:
http://en.wikipedia.org/wiki/Rank_(linear_algebra)
Come back and tell us what you had learnt and where you are stuck.
1 2 1
-2 -3 1
3 5 0
[COLOR=#252525][FONT=sans-serif]has rank 2: the first two rows are linearly independent, so the rank is at least 2, but all three rows are linearly dependent (the first is equal to the sum of the second and third) so the rank must be less than 3.
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Yes i seen the page.i can able to find the rank of matrix by converting it into echelon form and fixing the rank by looking non zero rows
what i dont understand is finding rank by finding independent column vectors. The below mentioned is extracted from wikipedia
it has been said that first two rows are independent so rank is 2 .i dont know how to find whether it is independent row vectors or dependent row vector and independent column vector or dependent column vectorCode:1 2 1 -2 -3 1 3 5 0 [COLOR=#252525][FONT=sans-serif]has rank 2: the first two rows are linearly independent, so the rank is at least 2, but all three rows are linearly dependent (the first is equal to the sum of the second and third) so the rank must be less than 3. [/FONT][/COLOR]
First, the page did not say 'it has been said that first two rows are independent so rank is 2.' The page said at least 2. It was only after it was noted that the first row was the sum of the second and third that the rank must be less than three and thus the rank was two.
Generally speaking, 'things' are linearly independent if no one of the 'things' can be written as a linear combination of the rest of the 'things' or, to put it a different way, if 'things' T1, T2, ..., and TN are linearly independent and
a1 T1 + a2 T2 + ... + an TN = [0]
then a1=a2=...=an=0. Note that the [0] is the zero 'thing'
In this particular case, the 'things' are matrix rows and we have
(-1) * Row1 + 1 * Row2 + 1 * Row3 = [0 0 0]
For your question, the 'things' are matrix columns and the [0] would be the zero column vector.