Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Examine the consistency of the system of equations 3x-y-2z = 2, 2y-z = -1, 3x-5y = -3.

Q : 5        Examine the consistency of the system of equations.

                \small 3x-y-2z=2

                \small 2y-z=-1

                \small 3x-5y=3

Answers (1)

best_answer

We have given the system of equations:

                                  \small 3x-y-2z=2

                                    \small 2y-z=-1

                                     \small 3x-5y=3

The given system of equations can be written in the form of matrix; AX =B

where A = \begin{bmatrix} 3& -1&-2 \\ 0& 2& -1\\ 3& -5 &0 \end{bmatrix},  X = \begin{bmatrix} x\\y \\ z \end{bmatrix}  and B = \begin{bmatrix} 2\\-1 \\ 3 \end{bmatrix}.

So, we want to check for the consistency of the equations;

|A| = 3(0-5) -(-1)(0+3)-2(0-6)

= -15 +3+12 = 0 

Therefore matrix A is a singular matrix.

So, we will then check (adjA)B,

(adjA) = \begin{bmatrix} -5 &10 &5 \\ -3& 6 & 3\\ -6& 12 & 6 \end{bmatrix}

\therefore (adjA)B = \begin{bmatrix} -5 &10 &5 \\ -3& 6 & 3\\ -6& 12 & 6 \end{bmatrix}\begin{bmatrix} 2\\-1 \\ 3 \end{bmatrix} = \begin{bmatrix} -10-10+15\\ -6-6+9 \\ -12-12+18 \end{bmatrix} = \begin{bmatrix} -5\\-3 \\ -6 \end{bmatrix} \neq 0

As, (adjA)B is non-zero thus the solution of the given system of the equation does not exist. Hence, the given system of equations is inconsistent.

Posted by

Divya Prakash Singh

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

Board Exam Time Table 2025 Live: UP Board exams from February 24; CBSE, BSEB date sheet soon
anam-khan

CBSE Date Sheet 2025 Live: Class 10, 12 board exam dates soon; syllabus, sample papers
anam-khan

Extra time in CBSE exams for students with type 1 diabetes: Kerala SHRC seeks report on plea

Latest Question