Using elementary row and coloumn transformation compute rank of following matrices: #((25,31,17,43),(75,94,53,132),(75,94,54,134),(25,32,20,48))# ?

1 Answer
Jul 28, 2018

Answer:

The #Rank (A)=3#

Explanation:

The matrix is

#A=((25,31,17,43),(75,94,53,132),(75,94,54,134),(25,32,20,48))#

Perform the following operations :

#R2larr(R2-3R1)# ; #R3larr(R3-3R1)# ; #R4larr(R4-3R1)#

#=((25,31,17,43),(0,1,2,3),(0,1,3,5),(0,1,3,5))#

#R4larr(R4-R3)# ; #R3larr(R3-R2)#

#=((25,31,17,43),(0,1,2,3),(0,0,1,2),(0,0,0,0))#

#R1larr(R1)/25#

#=((1,1.24,0.68,1.72),(0,1,2,3),(0,0,1,2),(0,0,0,0))#

Since there are #3# non -zero rows, the

#Rank(A)=3#