Rank of Matrix Questions 3





In this page rank of matrix questions 3 we are going to see solution of question3.

Procedure to find Echelon form (triangular form)

(i) The first element of every non-zero row is 1.

(ii) The row which is having every element zero should be below the non zero row.

(iii) Number of zeroes in the next non zero row should be more than the number of zeroes in the previous non zero row.

Question 3:

 
2 5 7 52
1 1 1 9
2 1 -1 0
 


Solution:

˜
 
2 5 7 52
1 1 1 9
2 1 -1 0
 

R₁ <-> R₂

˜
 
1 1 1 9
2 5 7 52
2 1 -1 0
 

R₂ => R₂ - 2R₁

        2          5         7        52

         2          2         2        18

        (-)       (-)       (-)       (-)

      _______________________

       0        3          4        34

      ______________________

R => R - 2R₁

         2          1         -1        0

         2          2         2        18

        (-)       (-)       (-)       (-)

      _______________________

       0        -1        -3       -18

      _______________________

˜
 
1 1 1 9
0 3 4 34
0 -1 -3 -18
 

R => 3R+ R₂

       0          -3         -9        -54

         0           3          4         34

        (-)          (-)       (-)       (-)

      _________________________

       0          0        -5        -20

      ________________________

˜
 
1 1 1 9
0 3 4 34
0 0 -5 -20
 

Number of non zero rows is 3. So rank of the given matrix = 3.Now you can try the following questions to understand this topic much better.










Questions



Solution


1) Find the rank of the following matrix

 
2 1 1 5
1 1 1 4
1 -1 2 1
 

Solution

2) Find the rank of the following matrix

 
1 2 1 7
2 -1 2 4
1 1 -2 -1
 

Solution

4) Find the rank of the following matrix

 
3 1 -1 2
2 -1 2 6
2 1 -2 -2
 

rank of matrix questions 3 rank of matrix questions 3

Solution

5) Find the rank of the following matrix

 
2 -1 3 9
1 1 1 6
1 -1 1 2
 

Solution







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