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ESE 2020: Engg. Mathematics Quiz 1

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Question 1

The eigen values of the matrix $Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\Civil Engg\Civil Engineeing-04-Apr\Civil-Engineering-2004_files\image085.png$

Question 2

In matrix equation [A] {X} = {R}.

and

One of the eigenvalues of matrix [A] is

Question 3

Given a 2 × 2 real matrix A with Eigen values i and –i. Then A cannot be

Question 4

The Eigen values of the matrix

are

Question 5

The following system of homogeneous equations
2x + y + 2z = 0
x + y + 3z = 0
4x + 3y + bz = 0
has non-trivial solution, then the value of ‘b’ is __.

Question 6

The value of a for which the following system has infinite solutions

Question 7

Consider the following equations
x + y + w = 0
y + z = 0
x + y + z + w = 0
x + y + 2z = 0
The system of equations will be

Question 8

Let the Eigen vector of the matrix

be written in the form

and

. What is the value of (a+b) ?

Question 9

Consider the following equations
3x – y – z + 2w = 0
3x + y – z – 2w = 0
12x + 3y – 4z – 6w = 0
The system of equations will be

Question 10

Consider the following system of equations in three real variables x₁, x₂ and x₃

The system of equations has:

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ESE & GATE CE Engineering Mathematics

Feb 24ESE & GATE CE