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  • need solution for RD Sharma maths class 12 chapter 5 Determinants exercise Fill in the blanks question 3

need solution for RD Sharma maths class 12 chapter 5 Determinants exercise Fill in the blanks question 3

Answers (1)

Answer: x = 4

Hint: Here, we use basic concept of singular matrix

Given: A=\begin{bmatrix} 1 &3 &x+2 \\ 2& 4 & 8\\ 3& 5& 10 \end{bmatrix} is singular

Solution: Here, A is regular

                So,  \left | A \right | is zero

                 \left | A \right |=0

So,

                \begin{bmatrix} 1 &3 &x+2 \\ 2& 4 & 8\\ 3& 5& 10 \end{bmatrix}=0

                1\begin{bmatrix} 4 & 8\\ 5& 10 \end{bmatrix}-3\begin{bmatrix} 2 & 8\\ 3& 10 \end{bmatrix}+(x+2)\begin{bmatrix} 2 & 4\\ 3& 5 \end{bmatrix}=0

                1(40-40)-3(20-24)+(x+2)(10-12)=0

                0-3(-4)+(x+2)(-2)=0

                12+\left [ -2x-4 \right ]=0

                8-2x=0

                8=2x

                x=\frac{8}{2}=4

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