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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

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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

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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

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

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

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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

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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

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

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

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

The Laplace transform of

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

For what value of k, the system linear equation has **no** solution

(3k + 1)x + 3y - 2 = 0

(k^{2} + 1)x + (k - 2)y - 5 = 0

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

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

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

The Inverse Laplace transform of is

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

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

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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

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

Laplace transform of the function sin ωt

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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

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

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

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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

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

Find the rank of the matrix**
**

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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

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

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

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

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

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

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

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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

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

The Laplace transform of g(t) is

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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

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