New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Matrices and Determinants question

2024 · 6 Apr · Shift 1 · Q54

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Matrices and Determinants
2024 · 6 Apr · Shift 1 · Q54

Matrices and Determinants question

2024 · 6 Apr · Shift 1 · Q54

JEE MainMathematicsMatrices and DeterminantsNumerical+4 / −1

Let

\alpha \beta \gamma=45 ; \alpha, \beta, \gamma \in \mathbb{R}

. If

x(\alpha, 1,2)+y(1, \beta, 2)+z(2,3, \gamma)=(0,0,0)

for some

x, y, z \in \mathbb{R}, x y z eq 0

, then

6 \alpha+4 \beta+\gamma

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

More from Matrices and Determinants

If $A$ is a square matrix of order 3 such that $det (A) = 3$ and $det (adj (- 4 adj (- 3 adj (3 adj ((2 A)^{- 1}))))) = 2^{m} 3^{n}$ …2024 · MCQ
If the system of equations $2 x + 7 y + λ z = 3 3 x + 2 y + 5 z = 4 x + μ y + 32 z = - 1$ has infinitely many solutions, then $(λ - μ)$ is equal to :2024 · Numerical
Let $A = 210 a 35 01 b$ . If $A^{3} = 4 A^{2} - A - 21 I$ , where $I$ is the identity matrix of order $3 \times 3$ , then $2 a + 3 b$ is equal to2024 · MCQ
Let $A = [21 - 1 1]$ . If the sum of the diagonal elements of $A^{13}$ is $3^{n}$ , then $n$ is equal to .2024 · Numerical
If $α e q a, β e q b, γ e q c$ and $α a a b β b c c γ = 0$ …2024 · MCQ
If the system of equations $x + 4 y - z = λ, 7 x + 9 y + μ z = - 3, 5 x + y + 2 z = - 1$ has infinitely many solutions, then $(2 μ + 3 λ)$ is equal to :2024 · MCQ
Let $λ, μ \in R$ . If the system of equations $3 x + 5 y + λ z = 3 7 x + 11 y - 9 z = 2 97 x + 155 y - 189 z = μ$ has infinitely many solutions, then $μ + 2 λ$ is equal to…2024 · MCQ
Let $A$ be a non-singular matrix of order 3. If $det (3 adj (2 adj ((det A) A))) = 3^{- 13} \cdot 2^{- 10}$ and $det (3 adj (2 A)) = 2^{m} \cdot 3^{n}$ …2024 · Numerical