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+8 votes

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 (59.5k points)
edited by | 586 views

2 Answers

+15 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 (14.2k points)
edited by
If u ever doubt in exam that rank can also be zero or not, then Only Null matrix has rank zero.
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.
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.

$\begin{pmatrix} 1 &1 \\ 0 & 0 \end{pmatrix}$
0 votes
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 (93 points)

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