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

A= ⎡⎢⎣100010001⎤⎥⎦which of the following is true?


A

A is a periodic matrix with period 1

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

A is an idempotent matrix

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

A is a periodic matrix with period 2

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

A is not an idempotent matrix

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

The correct options are
A

A is a periodic matrix with period 1


B

A is an idempotent matrix


A=100010001is identity matrix and we know that I=I2=I3 and so on.

I=I2=Ik+1

Now for Ik+1=I we get k =0 which is not a positive integer.

Now to get the least positive integer we will equate Ik+1 to next higher power i.e. I2

So, IK+1=I2

i.e., k+1=2

So k=1.

Since K=1 is the least integer satisfying the condition. So above matrix is a periodic matrix with period1. So option A is correct.

Also we know that for Ak+1=A, if k=1 satisfies the mentioned condition then the matrix is also called as idempotent matrix. So the above matrix is an idempotent matrix. So option (b) is also correct.


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