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  • Need Solution for R.D.Sharma Maths Class 12 Chapter 7 Solution of Simultaneous Linear Equation Exercise Fill in the blank Question 1 Maths Textbook Solution.

Need Solution for R.D.Sharma Maths Class 12 Chapter 7 Solution of Simultaneous Linear Equation Exercise Fill in the blank Question 1  Maths Textbook Solution.

Answers (1)

Answer \rightarrow a=-1

Given \rightarrow Here given that x+a y=0, a z+y=0, a x+z-0 has infinitely  many solutions.

To find \rightarrow The value of a.

Hint \rightarrow Given system of the equation can be written as AX=0 then solve to find a.

Solution\rightarrow  We know that x+a y=0, a z+y=0, a x+z-0

Given system of linear equation can be written as AX=0 where,

A=\left[\begin{array}{lll} 1 & a & 0 \\ 0 & 1 & a \\ a & 0 & 1 \end{array}\right], X=\left[\begin{array}{l} x \\ y \\ z \end{array}\right] \text { and } 0=\left[\begin{array}{l} 0 \\ 0 \\ 0 \end{array}\right]

We know that for infinitely many solution D=0

\Rightarrow\left|\begin{array}{lll} 1 & a & 0 \\ 0 & 1 & a \\ a & 0 & 1 \end{array}\right|=0

Expanding along row 1 we get

\begin{aligned} &\Rightarrow 1(1-0)-a\left(0-a^{2}\right)+0(0-a)=0 \\ &\Rightarrow 1+a^{3}=0 \end{aligned}

\begin{aligned} &\Rightarrow a^{3}+1=0 \\ &\Rightarrow a^{3}=-1 \\ &\Rightarrow a=-1 \end{aligned}

This is required value of a

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