The Gateway to Computer Science Excellence
First time here? Checkout the FAQ!
x
+9 votes
757 views

The rank of the matrix $\begin{bmatrix} 1 & 1 \\ 0 & 0 \end{bmatrix}$ is

  1. $4$
  2. $2$
  3. $1$
  4. $0$
asked in Linear Algebra by Veteran (59.9k points)
edited by | 757 views

2 Answers

+16 votes
Best answer
Rank of this matrix is 1 as the determint of 2nd order matrix is 0 and 1st order matrix is non zero so rank is $1$.
answered by Boss (14.4k points)
edited by
+14
If u ever doubt in exam that rank can also be zero or not, then Only Null matrix has rank zero.
0
if we check no. of non zero rows , then the ranks becomes 1.   which way we should decide rank and what is the correct answer.
+3
Rank of a matrix is also defined as number of non-zero rows in echelon form.

And the given matrix is already in Echelon form.

$\begin{pmatrix} 1 &1 \\ 0 & 0 \end{pmatrix}$
+1 vote
Rank Of A Matrix Can be easily calculated by Calculating Order of Submatrix Having Determinant Not Equal to zero in the above submatrix of size 2*2 determinant turns out to be zero hence rank cannot be One but if we see for 1*1 submatrix we have [1] as submatrix whose determinant is not equal to zero hence Rank is 1 .
answered by (103 points)
Answer:

Related questions

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
47,886 questions
52,255 answers
182,152 comments
67,672 users