Published by:
CGP EDU Academic Team
Published on: August 14, 2026
If the trivial solution is the only solution of the system of equations
x – ky + z = 0
kx + 3y – kz = 0
3x + y – z = 0
then the set of all values of k is :
Text Solution
Verified by ExpertsThe correct answer is:
A
x – ky + z = 0
kx + 3y – kz = 0
3x + y – z = 0
this system will have non trivial solution if
= 0
1(– 3 + k) + k(– k + 3k) + 1 (k– 9) = 0
k – 3 + 2k 2 + k – 9 = 0
2k 2 + 2k – 12 = 0
k 2 + k – 6 = 0
k = – 3, k = 2
so the system of equations will have only trivial solution when k ∈ R – {2, – 3}
──────────────────────────────────────────────────────────────────────────────────────────
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
Let A be a 2 × 2 matrix.
Statement-1 : adj(adj
Let a, b, c be such that b(a + c) ≠ 0. If + = 0. Then the value of 'n' is –
The number of 3 × 3 non-singular matrices, with four entries as 1 and all other entries as 0, is
Let A be a 2 × 2 matrix with non-zero entries and let A 2 = I , where I is 2 × 2 identity matrix.
T…
Consider the system of linear equations :
x 1 + 2x 2 + x 3 = 3
2x 1 + 3x 2 + x 3 = 3
3x 1 + 5x 2 + …
Let A and B be two symmetric matrices of order 3.
Statement-1 : A(BA) and (AB)A are symmetric matri…