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

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Answer 1 · 2018-07-28T08:36:46

The $Rank (A)=3$

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

$Rank(A)=3$

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