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  • Explain solution RD Sharma class 12 chapter Solution of Simultaneous Linear Equation exercise 7.1 question 16 maths

Explain solution RD Sharma class 12 chapter Solution of Simultaneous Linear Equation exercise 7.1 question 16 maths

Answers (1)

Answer:

\begin{aligned} &x=2500, y=3000, z=4000 \end{aligned}

Given:

According to question

\begin{aligned} &2 x+4 y+3 z=29000 \\ &5 x+2 y+3 z=30500 \\ &x+y+z=9500 \end{aligned}

Hint:

X=A-1B is used to solve this problem.

And the determinant and co-factor of matrix A, take it’s transpose that will be Adj A using Adj A calculate A-1.

Solution:

\begin{aligned} &2 x+4 y+3 z=29000\; \; \; \; \; \; .......(1) \\ &5 x+2 y+3 z=30500\; \; \; \; \; \; .......(2) \\ &x+y+z=9500\; \; \; \; \; \; .......(3) \end{aligned}

From(1),(2),(3)

\begin{aligned} &{\left[\begin{array}{lll} 2 & 4 & 3 \\ 5 & 2 & 3 \\ 1 & 1 & 1 \end{array}\right]\left[\begin{array}{l} x \\ y \\ z \end{array}\right]=\left[\begin{array}{c} 29000 \\ 30500 \\ 9500 \end{array}\right]} \\ &\left(R_{1} \rightarrow R_{1}-R_{3}, R_{2} \rightarrow R_{2}-5 R_{3}\right) \end{aligned}

\begin{aligned} &{\left[\begin{array}{ccc} 1 & 3 & 2 \\ 0 & -3 & -2 \\ 1 & 1 & 1 \end{array}\right]\left[\begin{array}{l} x \\ y \\ z \end{array}\right]=\left[\begin{array}{c} 19500 \\ -17000 \\ 9500 \end{array}\right]} \\ &\left(R_{3} \rightarrow R_{3}-R_{1}\right) \end{aligned}

\begin{aligned} &{\left[\begin{array}{ccc} 1 & 3 & 2 \\ 0 & -3 & -2 \\ 0 & -2 & -1 \end{array}\right]\left[\begin{array}{l} x \\ y \\ z \end{array}\right]=\left[\begin{array}{c} 19500 \\ -17000 \\ -10000 \end{array}\right]} \\ &\left(R_{3} \rightarrow 3 R_{3}-2 R_{2}\right) \end{aligned}

\begin{aligned} &{\left[\begin{array}{ccc} 1 & 3 & 2 \\ 0 & -3 & -2 \\ 0 & 0 & 1 \end{array}\right]\left[\begin{array}{l} x \\ y \\ z \end{array}\right]=\left[\begin{array}{c} 19500 \\ -17000 \\ 4000 \end{array}\right]} \\ &z=4000 \\ &-3 y-2 z=-17000 \\ &-3 y-8000=-17000 \\ &-3 y=-9000 \\ &y=3000 \end{aligned}

\begin{aligned} &x+3 y+2 z=19500 \\ &x+9000+8000=19500 \\ &x=2500 \\ &\therefore x=2500, y=3000, z=4000 \end{aligned}

 

Posted by

Gurleen Kaur

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