Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Express as a sum of a symmetric and a skew symmetric m

Express A=\begin{bmatrix} 4 &-3 \\ 2& -1 \end{bmatrix} as a sum of a symmetric and a skew symmetric matrix.

 

 
 
 
 
 

Answers (1)

A=\begin{bmatrix} 4 &-3 \\ 2& -1 \end{bmatrix}

A^{T}=\left[\begin{array}{cc} 4 & 2 \\ -3 & -1 \end{array}\right] \\

P=\frac{A+A^{T}}{2}=\frac{1}{2}\left[\begin{array}{cc} 8 & -1 \\ -1 & -2 \end{array}\right] \\

P'=\frac{1}{2}\left[\begin{array}{cc} 8 & -1 \\ -1 & -2 \end{array}\right]=P\\

P\rightarrow $Symmetric matrix $\\

Q=\frac{A-A^{T}}{2}=\frac{1}{2}\left[\begin{array}{cc} 0 & -5 \\ 5 & 0 \end{array}\right] \\

Q'=\frac{1}{2}\left[\begin{array}{cc} 0 & 5 \\ -5 & 0 \end{array}\right] = -Q\\

Q\rightarrow $Skew -symmetric matrix $\\

\\ P+Q=\frac{1}{2}\left[\begin{array}{ll} 8 & -6 \\ 4 & -2 \end{array}\right]\\\\P+Q=\left[\begin{array}{cc} 4 & -3 \\ 2 & -1 \end{array}\right] \\\\P+Q=A

Hence A is written as sum of symmetric matrix (P) and skew-symmetric matrix(Q).

Posted by

Safeer PP

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Exam Date 2027 Highlights: Class 10, 12 exam dates soon on cbse.gov.in; private candidate form
anam-khan

CBSE 10th, 12th board exam schedule 2027: Sample papers, passing marks
anam-khan

CBSE Class 10, 12 Board Exam 2027: Schedule soon; passing marks, paper pattern

Latest Question