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  • Need Solution for R.D.Sharma Maths Class 12 Chapter determinants Exercise 5.2 Question 46 Maths Textbook Solution.

Need Solution for  R.D.Sharma Maths Class 12 Chapter determinants  Exercise 5.2 Question 46 Maths Textbook Solution.

Answers (1)

Answer: Proved

Hint Use determinant formula

Given: \left|\begin{array}{lll} a & b & c \\ x & y & z \\ p & q & r \end{array}\right|=\left|\begin{array}{lll} x & y & z \\ p & q & r \\ a & b & c \end{array}\right|=\left|\begin{array}{lll} y & b & q \\ x & a & p \\ z & c & r \end{array}\right|

Solution:

\begin{aligned} &\left|\begin{array}{lll} a & b & c \\ x & y & z \\ p & q & r \end{array}\right|=\left|\begin{array}{lll} x & y & z \\ p & q & r \\ a & b & c \end{array}\right| \\ &R_{1} \leftrightarrow R_{3}, R_{2} \leftrightarrow R_{1}, R_{3} \leftrightarrow R_{1} \\ &=(-)(-)\left|\begin{array}{lll} x & y & z \\ a & b & c \\ p & q & r \end{array}\right| \end{aligned}


For interchanging R2↔R3    
negative sign will be added

Now convert rows in columns and column in row
\begin{aligned} &\left|\begin{array}{lll} x & y & z \\ p & q & r \\ a & b & c \end{array}\right|=\left|\begin{array}{lll} x & p & a \\ y & q & b \\ z & r & c \end{array}\right| \\ &\text { Now } R_{1} \leftrightarrow R_{2}, C_{2} \leftrightarrow C_{3} \\ &(-)(-)\left|\begin{array}{lll} y & q & b \\ x & p & a \\ z & r & c \end{array}\right|=\left|\begin{array}{lll} y & b & q \\ x & a & p \\ z & c & r \end{array}\right| \end{aligned}


 

 

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