Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Need solution for RD Sharma maths class 12 chapter Solution of Simultaneous Linear Equation exercise 7.1 question 5

Need solution for RD Sharma maths class 12 chapter Solution of Simultaneous Linear Equation exercise 7.1 question 5

Answers (1)

Answer:

x=2 \quad , \quad y=-1 \quad , \quad z=4

Given:

\begin{aligned} &A=\left[\begin{array}{ccc} 1 & -1 & 0 \\ 2 & 3 & 4 \\ 0 & 1 & 2 \end{array}\right] \quad, \quad B=\left[\begin{array}{ccc} 2 & 2 & -4 \\ -4 & 2 & -4 \\ 2 & -1 & 5 \end{array}\right] \backslash \\ &x-y=3, \quad 2 x+3 y+4 z=17 \quad, \quad y+2 z=7 \end{aligned}

Hint:

For matrix multiply matrix A with matrix B, Then X=A-1B  is formula for which is used to solve this problem.

Solution:

        \begin{aligned} A B &=\left[\begin{array}{ccc} 1 & -1 & 0 \\ 2 & 3 & 4 \\ 0 & 1 & 2 \end{array}\right]\left[\begin{array}{ccc} 2 & 2 & -4 \\ -4 & 2 & -4 \\ 2 & -1 & 5 \end{array}\right] \\ &=\left[\begin{array}{lll} 6 & 0 & 0 \\ 0 & 6 & 0 \\ 0 & 0 & 6 \end{array}\right] \\ A B &=6\left[\begin{array}{lll} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right]=6 I_{3} \end{aligned}

        \begin{aligned} &\frac{1}{6} A B=I_{3} \\ &\left(\frac{1}{6} B\right) A=I_{3} \quad(\therefore A B=B A) \\ &A^{-1}=\frac{1}{6} B \\ &A^{-1}=\frac{1}{6}\left[\begin{array}{ccc} 2 & 2 & -4 \\ -4 & 2 & -4 \\ 2 & -1 & 5 \end{array}\right] \end{aligned}

        \begin{aligned} X &=A^{-1} B \\ &=\frac{1}{6}\left[\begin{array}{ccc} 2 & 2 & -4 \\ -4 & 2 & -4 \\ 2 & -1 & 5 \end{array}\right]\left[\begin{array}{c} 3 \\ 17 \\ 7 \end{array}\right] \\ &=\frac{1}{6}\left[\begin{array}{c} 6+34-28 \\ -12+34-28 \\ 6-17+35 \end{array}\right] \end{aligned}

        \begin{aligned} &{\left[\begin{array}{l} x \\ y \\ z \end{array}\right]=\frac{1}{6}\left[\begin{array}{c} 12 \\ -6 \\ 24 \end{array}\right]} \\ &x=2, y=-1, z=4 \end{aligned}

Posted by

Gurleen Kaur

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Class 12 board exams 2025 to have 50% competency-based questions; no change in 10th
anam-khan

CBSE Class 12 board exams 2024 over; expected result date, trends of last 10 years

Latest Question