## RANK OF MATRIX QUESTIONS 3

Rank of matrix questions 3 :

Here we are going to see how to solve the given matrix using the method rank of matrix.

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, the rank of the given matrix = 3.Now you can try the following questions for more practice.

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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