TG EAPCET 2024 (Online) 9th May Evening Shift | Matrices and Determinants Question 1 | Mathematics

If $\alpha, \beta$ and $\gamma$ are the roots of the equation $\left|\begin{array}{lll}x & 2 & 2 \\ 2 & x & 2 \\ 2 & 2 & x\end{array}\right|=0$ and $\min (\alpha, \beta, \gamma)=\alpha$, then $2 \alpha+3 \beta+4 \gamma$ is equal to

-6

-8

TG EAPCET 2024 (Online) 9th May Evening Shift

MCQ (Single Correct Answer)

-0

If $\mathrm{A}=\left[\begin{array}{lll}1 & 2 & 2 \\ 3 & 2 & 3 \\ 1 & 1 & 2\end{array}\right]$ and $\mathrm{A}^{-1}=\left[\begin{array}{lll}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right]$, then $\sum_{\substack{1 \leq i \leq 3 \\ 1 \leq j \leq 3}} a_{i j}=$

$\frac{2}{3}$

$\frac{1}{3}$

TG EAPCET 2024 (Online) 9th May Evening Shift

MCQ (Single Correct Answer)

-0

If $A X=D$ represents the system of linear equations $3 x-4 y+7 z+6=0,5 x+2 y-4 z+9=0$ and $8 x-6 y-z+5=0$, then

$\operatorname{Rank}(A)=\operatorname{Rank}([A D])=1$

$\operatorname{Rank}(A)=\operatorname{Rank}([A D])=2$

$\operatorname{Rank}(A)=\operatorname{Rank}([A D])=3$

Rank $(A) \neq \operatorname{Rank}([A D])$

TG EAPCET 2024 (Online) 9th May Evening Shift

MCQ (Single Correct Answer)

-0

If $(x, y, z)=(\alpha, \beta, \gamma)$ is the unique solution of the system of simultaneous linear equations $3 x-4 y+z+7=0$, $2 x+3 y-z=10$ and $x-2 y-3 z=3$, then $\alpha=$

-3

-1

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