Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

p is some matrix of order n and a is another matrix of the same order then what is 1. pap'(p'=p transpose) 2.pap-1(p-1=p inverse)

p is some matrix of order n and a is another matrix of the same order then what is


1. pap'(p'=p transpose)


2.pap-1(p-1=p inverse)

Grade:

1 Answers

SAGAR SINGH - IIT DELHI
879 Points
10 years ago

Dear vinay,

The transpose of a matrix ${\bf A}$, denoted by ${\bf A}^T$, is obtained by switching the positions of elements $a_{ij}$ and $a_{ji}$ for all $i,j \in \{1,\cdots,n\}$. In other words, the ith column of ${\bf A}$ becomes the ith row of ${\bf A}^T$, or equivalently, the ith row of ${\bf A}$ becomes the ith column of ${\bf A}^T$:

\begin{displaymath}{\bf A}^T=[{\bf a}_1 \cdots {\bf a}_n]^T= \left[ \begin{array}{c} {\bf a}_1^T  ..  .. {\bf a}_n^T \end{array} \right] \end{displaymath}


where vector ${\bf a}_i$ is the ith column of ${\bf A}$ and its transpose ${\bf a}_i^T$ is the ith row of ${\bf A}^T$.

For any two matrices ${\bf A}$ and ${\bf B}$, we have

\begin{displaymath}({\bf A}{\bf B})^T={\bf B}^T {\bf A}^T \end{displaymath}


If ${\bf AB}={\bf BA}={\bf I}$, where ${\bf I}$ is an identity matrix:

\begin{displaymath}{\bf I}=diag[1,\cdots,1]=\left[ \begin{array}{cccc} 1 & 0 &... ...\cdot & \cdot & \cdot  0 & 0 & \cdot & 1 \end{array} \right] \end{displaymath}


then ${\bf B}={\bf A}^{-1}$ is the inverse of ${\bf A}$. ${\bf A}^{-1}$ exists iff $ det({\bf A}) \neq 0 $, i.e., $ rank({\bf A}) = n $.

For any two matrices ${\bf A}$ and ${\bf B}$, we have

\begin{displaymath}({\bf AB})^{-1}={\bf B}^{-1}{\bf A}^{-1} \end{displaymath}


and

\begin{displaymath}({\bf A}^{-1})^T=({\bf A}^T)^{-1} \end{displaymath}

Please feel free to ask your queries here. We are all IITians and here to help you in your IIT JEE preparation.

All the best.

Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.

Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar  respectively : Click here to download the toolbar..

 

Askiitians Expert

Sagar Singh

B.Tech, IIT Delhi

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free