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

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

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

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  

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

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

The Laplace transform of  

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

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

(k² + 1)x + (k - 2)y - 5 = 0

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

The Inverse Laplace transform of   is         

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

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

Laplace transform of the function sin ωt            

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

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

The Laplace transform of the function sin² 2t is  

 Find the rank of the matrix 

The running integrator, given by             

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

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

The fundamental period of the discrete-time signal is 

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

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

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

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

g (t) can be expressed as                      

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

The Laplace transform of g(t) is                  

The Laplace transform of g(t) is     

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