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  • Explain solution RD Sharma class 12 chapter Solution of Simultaneous Linear Equation exercise 7.1 question 20 maths

Explain solution RD Sharma class 12 chapter Solution of Simultaneous Linear Equation exercise 7.1 question 20 maths

Answers (1)

Answer:

x=R s 1125, y=R s 1125, z=R s 4750

Given:

According to the question,

\begin{aligned} &x+x+y=7000 \\ &2 x+y=7000 \\ &26 x+17 y=110000 \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:

Let the amount deposited in each of the three accounts be Rs x, Rs y, Rs z respectively

Since the total amount deposited is Rs7000  

\begin{aligned} &x+x+y=7000\\ &2 x+y=7000\; \; \; \; \; \; \; .......(1)\\ &\text { Total amount interest is } R s 550\\ &\frac{5}{100} x+\frac{8}{100} x+\frac{17}{200} y=550 \end{aligned}

\begin{aligned} &26 x+17 y=110000\; \; \; \; \; \; \; ......(2)\\ &\text { The above system equation can be written in matrix from } A X=B\\ &\left[\begin{array}{cc} 2 & 1 \\ 26 & 17 \end{array}\right]\left[\begin{array}{l} x \\ y \end{array}\right]=\left[\begin{array}{c} 7000 \\ 11000 \end{array}\right]\\ &\text { Where } A=\left[\begin{array}{cc} 2 & 1 \\ 26 & 17 \end{array}\right] X=\left[\begin{array}{l} x \\ y \end{array}\right] \text { and } B=\left[\begin{array}{c} 7000 \\ 11000 \end{array}\right]\\ &\text { Now, }|A|=\left|\begin{array}{cc} 2 & 1 \\ 26 & 17 \end{array}\right|=34-26=8 \end{aligned}

Let\; c_{i j}\; be\; the\; co\! f\! actors\; o\! f\; elements\; a_{i j}\; in\; A=\left[a_{i j}\right] \\ Then \\ c_{11}=(-1)^{1+1} 17=17, c_{12}=(-1)^{1+2} 26=-26 \\ c_{21}=(-1)^{2+1}(1)=-1, c_{22}=(-1)^{2+2}(2)=2

\begin{aligned} &\operatorname{adj} A=\left[\begin{array}{cc} 17 & -26 \\ -1 & 2 \end{array}\right]^{T} \\ &=\left[\begin{array}{cc} 17 & -1 \\ -26 & 2 \end{array}\right] \\ &A^{-1}=\frac{1}{|A|} a d j A \\ &=\frac{1}{8}\left[\begin{array}{cc} 17 & -1 \\ -26 & 2 \end{array}\right] \end{aligned}

\begin{aligned} A^{-1} &=\frac{1}{|A|} a d j A \\ &=\frac{1}{8}\left[\begin{array}{cc} 17 & -1 \\ -26 & 2 \end{array}\right] \\ X=& A^{-1} B \end{aligned}

\begin{aligned} &{\left[\begin{array}{c} x \\ y \end{array}\right]=\frac{1}{8}\left[\begin{array}{cc} 17 & -1 \\ -26 & 2 \end{array}\right]\left[\begin{array}{c} 7000 \\ 110000 \end{array}\right]} \\ &{\left[\begin{array}{c} x \\ y \end{array}\right]=\frac{1}{8}\left[\begin{array}{c} 119000-110000 \\ -182000+220000 \end{array}\right]} \\ &{\left[\begin{array}{l} x \\ y \end{array}\right]=\frac{1}{8}\left[\begin{array}{c} 9000 \\ 38000 \end{array}\right]} \end{aligned}

\begin{aligned} &x=\frac{9000}{8} \text { and } y=\frac{38000}{8} \\ &x=1125 \text { and } y=4750 \end{aligned}

Hence the amount deposited in each of the three accounts is Rs1125, Rs1102, Rs4750

Posted by

Gurleen Kaur

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