wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The rank of the matrix 12524a412a+1 is

A
1 if a = 6
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
2 if a = 1
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
3 if a = 2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
1 if a = -6
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is 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

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon