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Consider the system of equations given below:
x + y = 2
2x + 2y = 5
This system has
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
Solution for the system defined by the set of equations
4y + 3z = 8;
2x – z = 2
and 3x + 2y =5 is
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^{T}Y)^{–1}P^{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
(k^{2} + 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 sin^{2} 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 discretetime 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
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61 videos113 docs94 tests
