6it is given in TMH and M.L Khanna both ......i read it but still could not understand it
14 Answers
62It is something like no of linearly independent rows in a matrix
I am not sure if it in the iit jee syllabus.
662It is given in almost all books..
See the thing is like if i gave you three equations
x+y+z+w=4
x+y=2
z+w=2
2x+2y+z+w=6
x+y+2z+2w=6
then effectively I am giving you only 2 equations!
1so how to decide how many u are actually giving...
like if there are 10 eqns....
how to know...
is it always one less ?
21Rank Of a Matrix and echelon Maatrix both were not DER in JEE '09 SYLL.
1Rank of a matrix : It is equal to the no. of rows (or coloumns) of d largest possible square matrix whose determinant is not equal to zero.
Eg : A = \begin{bmatrix} 1& 2& 0& 3\\ 1& -2& 3& 0\\ 0& 0& 4& 6\\ 2& 4& 0& 6 \end{bmatrix}
The rank of above matrix is 3 as fourth row is a multiple of first row n hence |A| = 0 ... Now considering any 3x3 matrix, we'll get the value of det. as non-zero. hence rank is 3 [[remember that if atleast one 3x3 matrix has a non-zero det. then it is considered for rank]]
hope dis clears ur doubt :)
1dis is what i read n followed these two years... ;) :P
correct me if i'm wrong :)
