Test Index

CBSE Class 12 Math 2023 All Sets Solved Paper

© examsnet.com
Question : 16 of 20
Marks: +1, -0
If 2054=P+Q\begin{array}{cc} 2 & 0 \\ 5 & 4 \end{array} = P + Q where P is a symmetric and Q is a skew symmetric matrix, then Q is equal to:
Solution:  
Let A = 2054\begin{array}{cc} 2 & 0 \\ 5 & 4 \end{array}
Any matrix can be written as the sum of a sum of symmetric matrix and a skew-symmetric matrix.
A =   12(A+AT)+  12(A−AT)\;\frac{1}{2}(A + A^T) + \;\frac{1}{2}(A - A^T)
Here Q =   12(A−AT)=  12(2054−2504)\;\frac{1}{2}(A - A^T) = \;\frac{1}{2} \left( \begin{array}{cc} 2 & 0 \\ 5 & 4 \end{array} - \begin{array}{cc} 2 & 5 \\ 0 & 4 \end{array} \right)
=  12(0−550)= \;\frac{1}{2} \left( \begin{array}{cc} 0 & -5 \\ 5 & 0 \end{array} \right)
∴Q=0−  52  520\therefore Q = \begin{array}{cc} 0 & -\;\frac{5}{2} \\ \;\frac{5}{2} & 0 \end{array}
© examsnet.com
Go to Question:
Prev Question
Next Question