Value of 'a' for which system of equation a^3x + (a + 1)^3y + (a + 2)^3 z = 0 ; ax + (

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3 and 4 .Determinants and Matrices

normal

The value of $'a'$ for which the system of equation $a^3x + (a + 1)^3y + (a + 2)^3 z = 0$ ; $ax + (a + 1)y + (a + 2)z = 0$ ; $x + y + z = 0$ has a non-zero solution is :-

$1$

$0$

$-1$

$2$

Solution

$\mathrm{d}_{1}=\mathrm{d}_{1}=\mathrm{d}_{3}=0 \Rightarrow \mathrm{D}_{1}=\mathrm{D}_{2}=\mathrm{D}_{3}=0$

$\mathrm{D}=\left|\begin{array}{ccc}{a^{3}} & {(a+1)^{3}} & {(a+2)^{3}} \\ {a} & {(a+1)} & {(a+2)} \\ {1} & {1} & {1}\end{array}\right|=0 \Rightarrow \mathrm{a}=-1$

Standard 12

Mathematics

The system of equations $(\sin\theta ) x + 2z = 0$ , $(\cos\theta ) x + (\sin\theta )y = 0$ , $(\cos\theta )y + 2z = a$ has

normal

The value of the determinant $\left| {\,\begin{array}{*{20}{c}}2&8&4\\{ – 5}&6&{ – 10}\\1&7&2\end{array}\,} \right|$is

normal

$\left| {\,\begin{array}{*{20}{c}}1&a&b\\{ – a}&1&c\\{ – b}&{ – c}&1\end{array}\,} \right| = $

easy

Let the system of linear equations $4 x+\lambda y+2 z=0$ ; $2 x-y+z=0$ ; $\mu x +2 y +3 z =0, \lambda, \mu \in R$ has a non-trivial solution. Then which of the following is true?

hard

(JEE MAIN-2021)

The system of equations $-k x+3 y-14 z=25$ $-15 x+4 y-k z=3$ $-4 x+y+3 z=4$ is consistent for all $k$ in the set

medium

(JEE MAIN-2022)

The value of $'a'$ for which the system of equation $a^3x + (a + 1)^3y + (a + 2)^3 z = 0$ ; $ax + (a + 1)y + (a + 2)z = 0$ ; $x + y + z = 0$ has a non-zero solution is :-

Solution

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