JEE Main 2023 (Online) 31st January Morning Shift | Matrices and Determinants Question 62 | Mathematics

Let $$A = \left( {\matrix{ 1 & 0 & 0 \cr 0 & 4 & { - 1} \cr 0 & {12} & { - 3} \cr } } \right)$$. Then the sum of the diagonal elements of the matrix $${(A + I)^{11}}$$ is equal to :

4094

2050

6144

4097

JEE Main 2023 (Online) 30th January Evening Shift

MCQ (Single Correct Answer)

-1

For $\alpha, \beta \in \mathbb{R}$, suppose the system of linear equations

$$ \begin{aligned} & x-y+z=5 \\ & 2 x+2 y+\alpha z=8 \\ & 3 x-y+4 z=\beta \end{aligned} $$

has infinitely many solutions. Then $\alpha$ and $\beta$ are the roots of :

$x^2+18 x+56=0$

$x^2-10 x+16=0$

$x^2+14 x+24=0$

$x^2-18 x+56=0$

JEE Main 2023 (Online) 30th January Evening Shift

MCQ (Single Correct Answer)

-1

Out of Syllabus

If $P$ is a $3 \times 3$ real matrix such that $P^T=a P+(a-1) I$, where $a>1$, then :

$|A d j P|=1$

$|A d j P|>1$

$|A d j P|=\frac{1}{2}$