+10 votes
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The rank of matrix $\begin{bmatrix} 0 & 0 & -3 \\ 9 & 3 & 5 \\ 3 & 1 & 1 \end{bmatrix}$ is:

1. $0$
2. $1$
3. $2$
4. $3$
asked
edited | 825 views

## 2 Answers

+18 votes
Best answer

Answer: $C$

Determinant comes out to be $0$. So, rank cannot be $3$. The minor $\begin{bmatrix} 3 & 5 \\[0.3em] 1 & 1 \\[0.3em] \end{bmatrix}$ $!=0$. So, rank is $2.$

(or)

if we do elementary row operations on the given matrix then we get

As the number of non zero row is $2$,then the rank of the matrix is also $2.$

answered by Boss (34.1k points)
edited
+1

if we do elementary row operation then we get :-

as the number of non zero row is 2,then the rank of the matrix is also 2.

0
If any 2x2 minor is != 0 then we can say rank is 2. right?
0
This is a good example of how to calculate rank of a matrix by elementary row operation, not only for GATE but to clear doubt also.
+1
Wat is the operation done in 3rd matrix from left side ??
+2
R1-->3/2R2+ R1
0
Chk column wise, will give rank 2 in single step
–1 vote
Answer is C.
answered by (223 points)
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