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Question

The rank of the matrix 12524a412a+1 is

A
1 if a = 6
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B
2 if a = 1
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C
3 if a = 2
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D
1 if a = -6
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Solution

The correct options are
B 2 if a = 1
D 1 if a = -6
A=∣ ∣12524a412a+1∣ ∣=∣ ∣00a+600a612a+1∣ ∣
(Operating (R1R1+R3andR2R22R3)
=∣ ∣00000a612a+1∣ ∣(Operating R1R1+R2)
When a=6,A=∣ ∣000000125∣ ∣, ρ(A)=1
Where ρ(A)number of non-zero rows
When a=6,A=∣ ∣0000012127∣ ∣,ρ(A)=2
When a=1,A=∣ ∣000007122∣ ∣,ρ(A)=2
When a=2,A=∣ ∣000008122∣ ∣,ρ(A)=2

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