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  • Explain solution RD Sharma class 12 chapter 7 Solution of Simultaneous Linear Equation Exercise Fill in the blank Question 7 Maths Textbook Solution.

Explain solution RD Sharma class 12 chapter 7 Solution of Simultaneous Linear Equation Exercise Fill in the blank Question 7 Maths Textbook Solution.

Answers (1)

Answer \rightarrow k \neq 0, k=\pm 1, \pm 2, \pm 3, \pm 4, \ldots \ldots . \pm n

Given \rightarrow Given that the system of equations x+y+z=2,2 x+y-z=3 \text { and } 3 x+2 y+k z=4 has a unique solution.

To find \rightarrow We have to find the real value of k

Hint \rightarrow If the system of equations has a unique solution \Rightarrow|A| \neq 0

Solution \rightarrow We have system of equation,

\begin{aligned} &x+y+z=2 \\ &2 x+y-z=3 \\ &3 x+2 y+k z=4 \end{aligned}

Then,

\Rightarrow A=\left[\begin{array}{ccc} 1 & 1 & 1 \\ 2 & 1 & -1 \\ 3 & 2 & k \end{array}\right]

We know that the system of equations has a unique solution.

              \Rightarrow \left | A \right | should not be zero

\text { i.e. }|A| \neq 0

                \Rightarrow\left|\begin{array}{ccc} 1 & 1 & 1 \\ 2 & 1 & -1 \\ 3 & 2 & k \end{array}\right| \neq 0

                \begin{aligned} &\Rightarrow 1(k+2)-1(2 k+3)+1(4-3) \neq 0 \\ &\Rightarrow k+2-2 k-3+1 \neq 0 \\ &\Rightarrow-k \neq 0 \\ &\Rightarrow k=\pm 1, \pm 2, \ldots \ldots \pm n \end{aligned}

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