Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

How to find the rank of a matrix??

How to find the rank of a matrix??

Grade:12

1 Answers

SAGAR SINGH - IIT DELHI
879 Points
10 years ago

Dear eshita,

The rank of a matrix is the maximum number of independent rows (or, the maximum number of independent columns). A square matrix An×n is non-singular only if its rank is equal to n.

 

Determine the row-rank of

$ A = \begin{bmatrix}1 & 2 & 1 \\ 2 & 3 & 1 \\ 1 & 1 & 2 \end{bmatrix}.$
Solution: To determine the row-rank of $ A,$ we proceed as follows.

  1. $ \begin{bmatrix}1 & 2 & 1 \\ 2 & 3 & 1 \\ 1 & 1 & 2 \end{bmatrix} \overrightarr... ..._{31}(-1)} \begin{bmatrix}1 & 2 & 1 \\ 0 & -1 & -1 \\ 0 & -1  & 1 \end{bmatrix}.$
  2. $ \begin{bmatrix}1 & 2 & 1 \\ 0 & -1 & -1 \\ 0  & -1 & 1 \end{bmatrix} \overright... ..., R_{32}(1) } \begin{bmatrix}1 & 2 & 1 \\ 0 & 1 & 1 \\ 0 & 0 &  2 \end{bmatrix}.$
  3. $ \begin{bmatrix}1 & 2 & 1 \\ 0 & 1 & 1 \\ 0 &  0 & 2 \end{bmatrix}\overrightarro... ...R_{12}(-2) } \begin{bmatrix}1 & 0 & -1 \\ 0 & 1 & 1 \\ 0 & 0  & 1 \end{bmatrix}.$
  4. $ \begin{bmatrix}1 & 0 & -1 \\ 0 & 1 & 1 \\ 0  & 0 & 1 \end{bmatrix}\overrightarr... ...1), R_{13}(1)}\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} $

The last matrix  is the row reduced form of $ A$ which has $ 3$ non-zero rows. Thus,

$ {\mbox{row-rank}}(A)~=~3.$

 

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.

Please feel free to post as many doubts on our discussion forum as you can.we will get you the answer and detailed  solution very  quickly.

All the best.

Regards,
Askiitians Experts
Sagar Singh



Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free