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  • Please Solve RD Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Very Short Asnwer Question 22 Maths Textbook Solution

Please Solve RD Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Very Short Asnwer Question 22 Maths Textbook Solution

Answers (1)

Answer: \sum _{i}\sum _{j}a_{ij}=0

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

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

Solution:

a_{ij}=-a_{ji}  \left [ For \: all \: values \: of \: i,j\right ]a_{ii} =-a_{ii} \left [ For\: all\: values \: of \: i \right ]a_{ii}=0

Now,

\sum _{i}\sum_{j}a_{ij}=a_{11}+a_{12}+a_{13}+\cdot \cdot \cdot \cdot \cdot +a_{21}

              a_{ij}=a_{11}+a_{12}+a_{13}+\cdot \cdot \cdot \cdot \cdot -a_{12}

\sum _{i}\sum_{j}a_{ij}=0

              a_{ij}=0

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