Email
Chat with tutor
logo

Ask Questions, Get Answers

X
 
Answer
Comment
Share
Q)

If $I$ is the unit matrix of order $n$. Where$K\neq 0$ is a constsnt , then adj (KI)=

\[\begin{array}{1 1}(1) K^{n}(adj I)&(2)K(adj I)\\(3)K^{2}(adj(I))&(4)K^{n-1}(adj I)\end{array}\]

1 Answer

Comment
A)
I is a unit matrix of order n.
$KI= \begin{bmatrix} K & 0 & 0 &.... & 0 \\0 & K & 0 & .... & 0 \\ | &.... & .... & .... & | \\ 0 & 0 & 0 & .... & K \end{bmatrix}$
Co factor matrix of $KI$
$\qquad= \begin{bmatrix} K^{n-1} & 0 & 0 &.... & 0 \\0 & K^{n-1} & .... & .... & 0 \\ | &.... & .... & .... & .... \\ 0 & 0 & 0 & .... & K^{n-1} \end{bmatrix}$
$\qquad=K^{n-1} \begin{bmatrix} 1& 0 & 0 &.... & 0 \\0 & 1 & .... & .... & 0 \\ | &.... & .... & .... & .... \\ 0 & 0 & 0 & .... & 1 \end{bmatrix}$
$K^{n-1}(adj I)$
Hence 4 is the correct answer.
Help Clay6 to be free
Clay6 needs your help to survive. We have roughly 7 lakh students visiting us monthly. We want to keep our services free and improve with prompt help and advanced solutions by adding more teachers and infrastructure.

A small donation from you will help us reach that goal faster. Talk to your parents, teachers and school and spread the word about clay6. You can pay online or send a cheque.

Thanks for your support.
Continue
Please choose your payment mode to continue
Home Ask Homework Questions
Your payment for is successful.
Continue
Clay6 tutors use Telegram* chat app to help students with their questions and doubts.
Do you have the Telegram chat app installed?
Already installed Install now
*Telegram is a chat app like WhatsApp / Facebook Messenger / Skype.
...