GATE ME 2024 | Linear Algebra Question 3 | Engineering Mathematics

GATE ME 2024

MCQ (Single Correct Answer)

-1.33

The matrix $\begin{bmatrix} 1 & a \\ 8 & 3 \end{bmatrix}$ (where $a > 0$) has a negative eigenvalue if $a$ is greater than

$\frac{3}{8}$

$\frac{1}{8}$

$\frac{1}{4}$

$\frac{1}{5}$

GATE ME 2022 Set 2

MCQ (More than One Correct Answer)

-0

A is a 3 × 5 real matrix of rank 2. For the set of homogeneous equations Ax = 0, where 0 is a zero vector and x is a vector of unknown variables, which of the following is/are true?

The given set of equations will have a unique solution.

The given set of equations will be satisfied by a zero vector of appropriate size.

The given set of equations will have infinitely many solutions.

The given set of equations will have many but a finite number of solutions.

GATE ME 2022 Set 2

Numerical

-0

If the sum and product of eigenvalues of a 2 × 2 real matrix $\begin{bmatrix}3&p\\\ p&q\end{bmatrix} $ are 4 and -1 respectively, then |p| is _______ (in integer).

Your input ____

GATE ME 2022 Set 1

MCQ (More than One Correct Answer)

-0

The system of linear equations in real (x, y) given by

$\rm \begin{pmatrix} \rm x & \rm y \end{pmatrix} \begin{bmatrix} 2 & 5- 2 α \\\ α & 1 \end{bmatrix} = \rm \begin{pmatrix} \rm 0 & \rm 0 \end{pmatrix} $

involves a real parameter α and has infinitely many non-trivial solutions for special value(s) of α. Which one or more among the following options is/are non-trivial solution(s) of (x, y) for such special value(s) of α ?

x = 2, y = −2

x = −1, y = 4

x = 1, y = 1

x = 4, y = −2