6u sure this not in syllabus???
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.
6it is given in TMH and M.L Khanna both ......i read it but still could not understand it
62It 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 :)
