IIT JAM Exam  >  IIT JAM Questions  >  If the system of equations x - ky - z = 0, kx... Start Learning for Free
If the system of equations x - ky - z = 0, kx - y - z = 0, x + y - z = 0 has a non-zero solution, then the possible values of k are
  • a)
    - 1, 2
  • b)
    1, 2
  • c)
    0, 1
  • d)
    - 1, 1
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
If the system of equations x - ky - z = 0, kx - y - z = 0, x + y - z =...
Solution:

Given system of equations:
x - ky - z = 0
kx - y - z = 0
x + y - z = 0

Let A be the coefficient matrix of the system of equations, i.e.,
A = [1 -k -1]
[k -1 -1]
[1 1 -1]

Let B = [x]
[y]
[z]

Then, the system of equations can be written as AB = 0.

For non-zero solution, the determinant of A must be zero, i.e., det(A) = 0.

Hence, we have:
det(A) = 1(-1)(-1) + k(-1)(-1) + (1)(k)(1) - (1)(-1)(1) - k(1)(-1) - (1)(1)(-1) = 0

Simplifying the above equation, we get:
k² - 2k - 2 = 0

Solving the above quadratic equation, we get:
k = (2 ± √8)/2 = 1 ± √2

Since k must be real, we have k = 1 - √2 or k = 1 + √2.

Therefore, the possible values of k are -1, 1 + √2 and 1 - √2.

But, we know that the system of equations has non-zero solution only if k = 1, as for k = -1, the system of equations become inconsistent and for k = 1 + √2 and k = 1 - √2, the system of equations become dependent.

Hence, the only possible value of k is 1.

Therefore, the correct option is (D).
Explore Courses for IIT JAM exam
If the system of equations x - ky - z = 0, kx - y - z = 0, x + y - z = 0 has a non-zero solution, then the possible values of k area)- 1, 2b)1, 2c)0, 1d)- 1, 1Correct answer is option 'D'. Can you explain this answer?
Question Description
If the system of equations x - ky - z = 0, kx - y - z = 0, x + y - z = 0 has a non-zero solution, then the possible values of k area)- 1, 2b)1, 2c)0, 1d)- 1, 1Correct answer is option 'D'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about If the system of equations x - ky - z = 0, kx - y - z = 0, x + y - z = 0 has a non-zero solution, then the possible values of k area)- 1, 2b)1, 2c)0, 1d)- 1, 1Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the system of equations x - ky - z = 0, kx - y - z = 0, x + y - z = 0 has a non-zero solution, then the possible values of k area)- 1, 2b)1, 2c)0, 1d)- 1, 1Correct answer is option 'D'. Can you explain this answer?.
Solutions for If the system of equations x - ky - z = 0, kx - y - z = 0, x + y - z = 0 has a non-zero solution, then the possible values of k area)- 1, 2b)1, 2c)0, 1d)- 1, 1Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for IIT JAM. Download more important topics, notes, lectures and mock test series for IIT JAM Exam by signing up for free.
Here you can find the meaning of If the system of equations x - ky - z = 0, kx - y - z = 0, x + y - z = 0 has a non-zero solution, then the possible values of k area)- 1, 2b)1, 2c)0, 1d)- 1, 1Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of If the system of equations x - ky - z = 0, kx - y - z = 0, x + y - z = 0 has a non-zero solution, then the possible values of k area)- 1, 2b)1, 2c)0, 1d)- 1, 1Correct answer is option 'D'. Can you explain this answer?, a detailed solution for If the system of equations x - ky - z = 0, kx - y - z = 0, x + y - z = 0 has a non-zero solution, then the possible values of k area)- 1, 2b)1, 2c)0, 1d)- 1, 1Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of If the system of equations x - ky - z = 0, kx - y - z = 0, x + y - z = 0 has a non-zero solution, then the possible values of k area)- 1, 2b)1, 2c)0, 1d)- 1, 1Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice If the system of equations x - ky - z = 0, kx - y - z = 0, x + y - z = 0 has a non-zero solution, then the possible values of k area)- 1, 2b)1, 2c)0, 1d)- 1, 1Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice IIT JAM tests.
Explore Courses for IIT JAM exam
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev