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Determinants

Question

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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

30

-10

10

-30

Solution

System fo equation has non-zero solution

$∴ |\begin{matrix} 1 & k & 3 \\ 3 & k & - 2 \\ 2 & 4 & - 3 \end{matrix}| = 0 \Rightarrow 44 - 4 k = 0 ∴ k = 11 L e t z = λ ∴ x = \frac{5 λ}{2}, y = - \frac{λ}{2}, z = λ ∴ \frac{x z}{y^{2}} = \frac{\frac{5 λ}{2} . λ}{{(- \frac{λ}{2})}^{2}} = 10$

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Determinants

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

30

-10

10

-30

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For Daily Free Study Material Join wiredfaculty

Determinants

If the system of linear equationsx + ky + 3z = 03x + ky – 2z = 02x + 4y – 3z = 0has a non-zero solution (x,y,z), then xz/y2 is equal to 30 -10 10 -30

Some More Questions From Determinants Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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

30

-10

10

-30