Question

Matrix a=|1 1 -1 ,3-2 3 ,2 -3 4|find the
rank of a matrix by row echelon form

Answer 1

A=

⎣

⎢

⎢

⎡

1

4

3

2

5

4

3

6

5

⎦

⎥

⎥

⎤

Here, ∣A∣=1−4+3=0

So, rank of matrix <3.

Now, we will reduce into Echelon form,

R

2

→R

2

−4R

1

⎣

⎢

⎢

⎡

1

0

3

2

−3

4

3

−6

5

⎦

⎥

⎥

⎤

R

3

→R

3

−3R

1

⎣

⎢

⎢

⎡

1

0

0

2

−3

−2

3

−6

−4

⎦

⎥

⎥

⎤

R

3

→R

3

−

3

2

R

2

⎣

⎢

⎢

⎡

1

0

0

2

−3

0

3

−6

0

⎦

⎥

⎥

⎤

R

2

→−

3

1

R

2

⎣

⎢

⎢

⎡

1

0

0

2

1

0

3

2

0

⎦

⎥

⎥

⎤

Here, there are 2 non-zero rows in the Echelon form of A.

Hence, rank =2

R

3

→R

3

−3R

1

⎣

⎢

⎢

⎡

1

0

0

2

−3

−2

3

−6

−4

⎦

⎥

⎥

⎤

R

3

→R

3

−

3

2

R

2

⎣

⎢

⎢

⎡

1

0

0

2

−3

0

3

−6

0

⎦

⎥

⎥

⎤

R

2

→−

3

1

R

2

⎣

⎢

⎢

⎡

1

0

0

2

1

0

3

2

0

⎦

⎥

⎥

⎤

Here, there are 2 non-zero rows in the Echelon form of A.

Hence, rank =2

HEY BRO ANSWER IS CORRECT THEN ONLY GIVE ME THE LIKE AND BRAINLIST ANSWER OK