Hey there! We receieved your request
Stay Tuned as we are going to contact you within 1 Hour
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-5470-145
+91 7353221155
Use Coupon: CART20 and get 20% off on all online Study Material
Complete Your Registration (Step 2 of 2 )
Sit and relax as our customer representative will contact you within 1 business day
OTP to be sent to Change
wat do trace and rank of a matrix mean?????
Dear Unnati,
Trace : Sum of the elements of A (square matrix of order n ) lying along the principle diagonal is called trace of A.
Ex - matrix = 1 0 so trace = 1+5 =6
0 5
Rank : No. r is said to be the rank of a m*n matrix A if,
1 every square sub matrix of order (r+1) or more is singular and
2 there exists at least one square submatrix of order r which is non singular
or rank of a matrix is the order of highest order non singular sub matrix
Ex - A = 1 2 3
4 5 6
3 4 5
we have det. A =0 so, r(A) is less then 3, also we have 5 6 a non singular square sub matrix of order 2 .
4 5
hence rank of A = 2
Please feel free to ask your queries here. We are all IITians and here to help you in your IIT JEE preparation.
All the best.
Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.
Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar respectively : Click here to download the toolbar..
Askiitians Expert
Anil Pannikar
IIT Bombay
Dear unnati,
Let be an square matrix:
where
is the jth column vector and
is the ith row vector.
The n rows span the row space of and the n columns span the column space of . The dimensions of these two spaces are the same and called the rank of :
The determinant of is denoted by
and we have
if and only if
.
The trace of is defined as the sum of its diagonal elements:
Please feel free to ask your queries here. We are all IITians and here to help you in your IIT JEE preparation. All the best. Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian. Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar respectively : Click here to download the toolbar.. Askiitians Expert Sagar Singh B.Tech, IIT Delhi
Sagar Singh
B.Tech, IIT Delhi
Get your questions answered by the expert for free
You will get reply from our expert in sometime.
We will notify you when Our expert answers your question. To View your Question
Win Gift vouchers upto Rs 500/-
Register Yourself for a FREE Demo Class by Top IITians & Medical Experts Today !