System of equations x+y+z=6 , x+2 y+5 z=9 , x+5 y+λ z=μ has no solution if

English

Gujarati

Hindi

3 and 4 .Determinants and Matrices

medium

The system of equations $x+y+z=6$, $x+2 y+5 z=9$, $x+5 y+\lambda z=\mu$ has no solution if

A$\lambda=17, \mu \neq 18$

B$\lambda \neq 17, \mu \neq 18$

C$\lambda=15, \mu \neq 17$

D$\lambda=17, \mu=18$

(JEE MAIN-2025)

Solution

$D=\left|\begin{array}{lll}1 & 1 & 1 \\ 1 & 2 & 5 \\ 1 & 5 & \lambda\end{array}\right|=0$
$\lambda=17$
$D_z=\left|\begin{array}{lll}1 & 1 & 6 \\ 1 & 2 & 9 \\ 1 & 5 & \mu\end{array}\right| \neq 0$
$\mu \neq 18$

Standard 12

Mathematics

If $\left| {\,\begin{array}{*{20}{c}}{{x^2} + x}&{x + 1}&{x – 2}\\{2{x^2} + 3x – 1}&{3x}&{3x – 3}\\{{x^2} + 2x + 3}&{2x – 1}&{2x – 1}\end{array}\,} \right| = Ax – 12$, then the value of $A $ is

medium

(JEE MAIN-2015)

If $\left| {\,\begin{array}{*{20}{c}}a&b&{a\alpha – b}\\b&c&{b\alpha – c}\\2&1&0\end{array}\,} \right| = 0$ and $\alpha \ne \frac{1}{2},$ then

medium

$A=\left[\begin{array}{lll}1 & 0 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 4\end{array}\right],$ then show that $|3 A|=27|A|$.

easy

If the system of equations $2 x-y+z=4$, $5 x+\lambda y+3 z=12$,$100 x-47 y+\mu z=212$ has infinitely many solutions, then $\mu-2 \lambda$ is equal to

medium

(JEE MAIN-2025)

The existence of the unique solution of the system $x + y + z = \lambda ,$ $5x – y + \mu z = 10$, $2x + 3y – z = 6$ depends on

medium

The system of equations $x+y+z=6$, $x+2 y+5 z=9$, $x+5 y+\lambda z=\mu$ has no solution if

Solution

Similar Questions

If $\left| {\,\begin{array}{*{20}{c}}{{x^2} + x}&{x + 1}&{x – 2}\\{2{x^2} + 3x – 1}&{3x}&{3x – 3}\\{{x^2} + 2x + 3}&{2x – 1}&{2x – 1}\end{array}\,} \right| = Ax – 12$, then the value of $A $ is

If $\left| {\,\begin{array}{*{20}{c}}a&b&{a\alpha – b}\\b&c&{b\alpha – c}\\2&1&0\end{array}\,} \right| = 0$ and $\alpha \ne \frac{1}{2},$ then

$A=\left[\begin{array}{lll}1 & 0 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 4\end{array}\right],$ then show that $|3 A|=27|A|$.

If the system of equations $2 x-y+z=4$, $5 x+\lambda y+3 z=12$,$100 x-47 y+\mu z=212$ has infinitely many solutions, then $\mu-2 \lambda$ is equal to

The existence of the unique solution of the system $x + y + z = \lambda ,$ $5x – y + \mu z = 10$, $2x + 3y – z = 6$ depends on

Start a Free Trial Now