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Please Solve RD Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Very Short Asnwer Question 21 Maths Textbook Solution.

Answers (1)

Answer: $\sum _{i}a_{ii}=0$

Hint: Here to solve this we use the basic concept of skew symmetric matrix

Given: $A=\left [ a_{ij} \right ]$ is skew symmetric

Write value of $\sum _{i}a_{ii}=?$

Solution: Let $A$ is a $m\times n$ matrix

Where $a_{ij}=i$ denotes row

J denotes column

$I=\sum _{i=1}^{m}a_{ii}$

$=a_{11}+a_{22}+a\cdot \cdot \cdot \cdot \cdot a_{mn}$

$A=\left [ a_{ij} \right ]_{m\times n} where\: i\leq m,j\leq n$

Here $A$ is skew symmetric

So, $-A=A^{T}$

$-a_{ij}=a_{ji}$

$2a_{ij}=0$

$a_{ij}=0$

So, if $j=i$

$a_{ii}=0$

So, $\sum _{i}a_{ii}=0$

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