Question

find the rank of the matrix (2,-1,3,1)(1,4,-2,1)(5,2,4,3,)​

Answer 1

Step-by-step explanation:

Given A=

⎣

⎢

⎢

⎡

2

0

0

3

1

−2

1

2

−4

4

−1

2

⎦

⎥

⎥

⎤

Rank of A ≤min 3,4

So, rank of A≤3

Now, we will reduce it to Echelon form

R

3

→R

3

+2R

2

⎣

⎢

⎢

⎡

2

0

0

3

1

0

1

2

0

4

−1

0

⎦

⎥

⎥

⎤

Here, row R

3

has all elements 0.

So, two non-zero rows.

Hence, rank =2