CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If matrix, A=1-32k and A2-4A+10I=A, then k=


A

0

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

-4

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

4 but not 1

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D

1 or 4

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C

4 but not 1


Explanation for the correct option

The given matrix is A=1-32k.

The given equation is A2-4A+10I=A

1-32k×1-32k-41-32k+101001=1-32k1×1+-3×2-3×1+-3×k2×1+k×2-3×2+k×k+-412-8-4k+100010=1-32k-5-3k-32k+2k2-6+-4+1012+0-8+0-4k+10=1-32k-5+6-3k-3+122k+2-8k2-6-4k+10=1-32k1-3k+92k-6k2-4k+4=1-32k

Compare both sides,

-3k+9=-3...12k-6=2...2k2-4k+4=k...3

Consider the equation 3.

k2-4k+4=kk2-5k+4=0k2-4k-k+4=0kk-4-1k-4=0k-4k-1=0k=1,4

But k=1 does not satisfy equation 1 and 2.

Therefore, the value of k is equal to 4 but not 1.

Hence, option(C) is the correct option.


flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Transpose of a Matrix
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon