Question

find the Rank 여 matrix
A= ( 4 2 1 3
6 3 4 7
2 1 0 7 )​

Answer 1

Answer:

The rank of matrix A is 3, since there are three nonzero rows in its row echelon form.

Step-by-step explanation:

To find the rank of matrix A, we perform row operations to bring A to its row echelon form, and then count the number of nonzero rows. The row echelon form of A can be found as follows:

R2 = R2 - 3/2 R1

R3 = R3 - 1/2 R1

(4 2 1 3)

(0 1/2 7/2 1/2)

(0 0 -7 6 )

R3 = -1/7 R3

(4 2 1 3 )

(0 1/2 7/2 1/2)

(0 0 1 -6/7)

R2 = R2 - 7/2 R3

R1 = R1 - R3 - R2

(4 2 0 16/7)

(0 1/2 0 -11/14)

(0 0 1 -6/7 )

R1 = R1 - 2R2

(4 0 0 39/14)

(0 1/2 0 -11/14)

(0 0 1 -6/7 )

Therefore, the rank of matrix A is 3, since there are three nonzero rows in its row echelon form.

To learn more about similar question visit:

https://brainly.in/question/54095859?referrer=searchResults

https://brainly.in/question/34980326?referrer=searchResults

#SPJ1