Civil Engineering (CE) > Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2

Test Description

Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 for Civil Engineering (CE) 2023 is part of Civil Engineering (CE) preparation. The Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 questions and answers have been prepared
according to the Civil Engineering (CE) exam syllabus.The Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 MCQs are made for Civil Engineering (CE) 2023 Exam.
Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 below.

Solutions of Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 questions in English are available as part of our course for Civil Engineering (CE) & Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 solutions in
Hindi for Civil Engineering (CE) course.
Download more important topics, notes, lectures and mock test series for Civil Engineering (CE) Exam by signing up for free. Attempt Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 | 30 questions in 90 minutes | Mock test for Civil Engineering (CE) preparation | Free important questions MCQ to study for Civil Engineering (CE) Exam | Download free PDF with solutions

1 Crore+ students have signed up on EduRev. Have you? Download the App |

Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 1

Consider the system of equations given below:

x + y = 2

2x + 2y = 5

This system has

Detailed Solution for Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 1

(b) This can be written as AX = B Where A

Angemented matrix

rank(A) ≠ rank(). The system is inconsistant .So system has no solution.

Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 2

For what value of a, if any, will the following system of equations in x, y and z have a solution?

2x + 3y = 4

x+y+z = 4

x + 2y - z = a

Detailed Solution for Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 2

(b)

If a = 0 then rank (A) = rank() = 2. Therefore the system is consistant

∴ The system has sol^{n} .

Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 3

Solution for the system defined by the set of equations

4y + 3z = 8;

2x – z = 2

and 3x + 2y =5 is

Detailed Solution for Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 3

Ans.(d)

Consider the matrix A = ,Now det (A) = 0

So byCramer's Rule the system has no solution

Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 4

For what values of α and β the following simultaneous equations have an infinite numberof solutions?

x + y + z = 5; x + 3y + 3z = 9; x + 2y + αz = β

Detailed Solution for Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 4

(d)

=

For infinite solution of the system

α − 2 = 0 and β − 7 = 0

⇒ α = 2 and β = 7.

Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 5

Let A be a 3 × 3 matrix with rank 2. Then AX = 0 has

Detailed Solution for Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 5

(b)

We know , rank (A) + Solution space X(A) = no. of unknowns.

⇒2 + X(A) = 3 . [Solution space X(A)= No. of linearly independent vectors]

⇒ X(A) =1.

Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 6

A is a 3 x 4 real matrix and A x = b is an inconsistent system of equations. The highest possible rank of A is

Detailed Solution for Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 6

(b). Highest possible rank of A= 2 ,as Ax = b is an inconsistent system.

Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 7

Consider the matrices X _{(4 × 3)}, Y_{ (4 × 3)} and P_{ (2 × 3)}. The order or P (X^{T}Y)^{–1}P^{T}] ^{T} will be

Detailed Solution for Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 7

(a)

Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 8

Given matrix [A] = the rank of the matrix is

Detailed Solution for Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 8

(c)

∴Rank(A) = 2

Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 9

The Laplace transform of

Detailed Solution for Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 9

Ans. (b)False

Laplace transform of

Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 10

There are two containers, with one containing 4 Red and 3 Green balls and the other containing 3 Blue and 4 Green balls. One bal is drawn at random form each container.The probability that one of the ball is Red and the other is Blue will be

Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 11

If L defines the Laplace Transform of a function, L [sin (at)] will be equal to

Detailed Solution for Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 11

Ans. (b)

⇒

Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 12

The Inverse Laplace transform of is

Detailed Solution for Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 12

Ans. (c)

Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 13

Laplace transform for the function f(x) = cosh (ax) is

Detailed Solution for Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 13

Ans. (b)

It is a standard result that

L (cosh at) =

Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 14

If F(s) is the Laplace transform of function f (t), then Laplace transform of

Detailed Solution for Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 14

Ans. (a)

Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 15

Laplace transform of the function sin ωt

Detailed Solution for Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 15

Ans. (b)

Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 16

Laplace transform of (a + bt)^{2} where ‘a’ and ‘b’ are constants is given by:

Detailed Solution for Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 16

Ans.(c)

Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 17

A delayed unit step function is defined as Its Laplace transform is

Detailed Solution for Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 17

Ans. (d)

Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 18

The Laplace transform of the function sin^{2} 2t is

Detailed Solution for Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 18

Ans.(a)

Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 19

Find the rank of the matrix** **

Detailed Solution for Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 19

To find out the rank of the matrix first find the |A|

If the value of the |A| = 0 then the matrix is said to be reduced

But, as the determinant of A has some finite value, then the rank of the matrix is 3.

Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 20

The running integrator, given by

Detailed Solution for Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 20

Ans. (b)

Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 21

The state transition matrix for the system X^{-} = AX with initial state X(0) is

Detailed Solution for Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 21

Ans. (c)

Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 22

The Fourier transform of x(t) = e^{–at} u(–t), where u(t) is the unit step function

Detailed Solution for Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 22

Ans. (d)

Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 23

The fundamental period of the discrete-time signal is

Detailed Solution for Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 23

Ans. (b)

or

or

Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 24

u(t) represents the unit step function. The Laplace transform of u(t – ζ) is

Detailed Solution for Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 24

Ans. (c)

f(t) = u(t – ζ)

L{f(t)} = L{u(t – ζ)}

Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 25

The fundamental period of x(t) = 2 sin πt + 3 sin 3πt, with t expressed in seconds, is

Detailed Solution for Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 25

Ans. (d)

H.C.F. of 2π and 3π is 6π.

Then, fundamental frequency = 6π

∴ Period, T = = 3 sec

Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 26

If the Fourier transform of x[n] is X(e^{jω}), then the Fourier transform of (–1)n x[n] is

Detailed Solution for Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 26

Ans. (c)

Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 27

Given f(t) and g(t) as shown below:

g (t) can be expressed as

Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 28

Given f(t) and g(t) as shown below:

The Laplace transform of g(t) is

Detailed Solution for Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 28

Ans. (c)

Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 29

The Laplace transform of g(t) is

Detailed Solution for Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 29

Ans. (c)

Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 30

Let Y(s) be the Laplace transformation of the function y (t), then final value of the function is

Detailed Solution for Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 - Question 30

Ans. (c)

Information about Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 Page

In this test you can find the Exam questions for Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2 solved & explained in the simplest way possible.
Besides giving Questions and answers for Test: Systems of Linear Equations, Matrix Algebra & Transform Theory- 2, EduRev gives you an ample number of Online tests for practice

Download as PDF