Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
+1 vote
2.7k views
in Matrices & determinants by (54.8k points)

If the system of linear equations x + ky + 3z = 0; 3x + ky – 2z = 0; 2x + 4y – 3z = 0 has a non-zero solution (x, y, z), then xz/y2 is equal to 

(A) 10 

(B) – 30 

(C) 30 

(D) –10

1 Answer

+1 vote
by (52.5k points)
selected by
 
Best answer

Answer is (A) 10

Given:

x + ky + 3z = 0, 3x + ky – 2z = 0, 2x + 4y – 3z = 0

For non-zero solutions, we know that

−3k + 8 – k(−9 + 4) + 3(12 – 2k) = 0

−3k + 8 + 5k + 36 – 6k = 0

−4k = −44 k = 11

Therefore, x + 11y + 3z = 0

3x + 11y + 2z = 0

2x + 4y – 3z = 0

Now, z = t; therefore,

x + 11y = −3t

3x + 11y = 2t

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...