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  • Please solve RD Sharma class 12 chapter 5 Determinants exercise Fill in the blanks question 29 maths textbook solution

Please solve RD Sharma class 12 chapter 5 Determinants exercise Fill in the blanks question 29 maths textbook solution

Answers (1)

Answer: AP

Hint: Here, we use basic concept of determinant of matrix.

Given: \left[\begin{array}{ccc} x+1 & x+2 & x+a \\ x+2 & x+3 & x+b \\ x+3 & x+4 & x+c \end{array}\right]=0

Solution:

            So, Let’s

                            \begin{aligned} &R_{2} \rightarrow R_{2}-R_{1} \\ &R_{3} \rightarrow R_{3}-R_{1} \\ &{\left[\begin{array}{ccc} x+1 & x+2 & x+a \\ 1 & 1 & b-a \\ 2 & 2 & c-a \end{array}\right]=0} \end{aligned}

Let’s perform differentiate

                            \begin{aligned} &=x+a[0+0]-1[(0-a)-2(b-a)]+(x+a) 0=0 \\ &c+a-2 b=0 \\ &2 b=a+c \end{aligned}

So a,b,c are in A.P

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