1)

The rank of the matrix [12524a412a+1] is


A) 1 if a = 6

B) 2 if a = 1

C) 3 if a = 2

D) 1 if a = 4

Answer:

Option B

Explanation:

Let

A=[12524a412a+1][12500a+600a+6]

[R2  R2 + 2R1, R3 → R+R1]

Clearly rank of A is 1 if a = -6

Also, for a= 1, | A | = |125243122|=0

and |2543|=6+20=140

.'. rank of A is 2 if a = 1