All India Electronics and Communication Engineering (ECE) Group

If 1 and 3 are the eigenvalues of a square matrix A then A3 is equal to
  • a)
    13 (A - I2 )
  • b)
    13A - 12 I2
  • c)
    12 (A - I2)
  • d)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Saptarshi Nair answered  •  3 hours ago
Solution:

Given, the eigenvalues of matrix A are 1 and 3.

We need to find A^3.

Let's find the matrix A first.

Let v be an eigenvector of A corresponding to eigenvalue λ.
Then, Av = λv.

Let's find the eigenvectors corresponding to eigenvalues 1 and 3.

For λ = 1,

Av = v
⇒ A - I = 0
⇒ A = I

For λ =
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Show that point transformation between cylindrical and spherical?

Ishan Kapoor answered  •  yesterday
Point Transformation between Cylindrical and Spherical Coordinates

Cylindrical and spherical coordinates are two commonly used coordinate systems in mathematics and physics. It is often necessary to convert between these coordinate systems when solving problems. The point transformation between cylindrical and spherical coordinates can be done using the following steps:

1. Cy
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Consider a signal x(t) defined as
x(t) = sinc (100 πt) + 2 sinc2 (150 πt)
What will be the Nyquist sampling rate (in Hz) for this signal?
(Answer up to the nearest integer)
    Correct answer is '300'. Can you explain this answer?

    Gate Gurus answered  •  Feb 24, 2023
    X(t) = sinc (100 πt)+ 2 sinc2(150 πt)
    The sampling rate of sinc (100 πt)is
    fs1 = 2 fm1 = 2 x 100 = 200 Hz
    The sampling rate of sinc2 (150 πt) is
    fs2 = 2 fm2 = 2 x 150 = 300 Hz
    When both the signals are added, maximum frequency component will be 150 Hz. So, the sampling rate is 300 Hz.

    The unit-step response of a unity feedback system with open loop transfer function G(s) = K/((s + 1)(s + 2)) is shown in the figure below. What is the value of K? (Answer up to the nearest integer)
      Correct answer is '6'. Can you explain this answer?

      Gate Gurus answered  •  Feb 24, 2023
      From the figure we can see that steady state error for given system is
      Ess = 1 - 0.75 = 0.25
      Steady state error for unity feed back system is given by
      So, ess = 2/2 + K = 0.25
      2 = 0.5 + 0.25 K
      K = 1.5/0.25 = 6

      Given
      dy/dx = x2 − y2, y(0)
      The value of y(0/1) using Runge-kutta Second order method is (Take h = 0.1)
      • a)
        0.89
      • b)
        0.93
      Correct answer is between '0.89,0.93'. Can you explain this answer?

      Machine Experts answered  •  Feb 24, 2023
      Y’ = x2 - y2
      y(0) = 1
      y1p = y0 + h.f (xo,yo)
      =1 + 0.1(-1) = 0.9
      Modified value of y1 is
      y1c= y0+ h/2 [f(x0,y0) + f(x1,y1p)]
      =1+ 0.1/2[-1 + (0.01 - 0.81)]
      =1 - 0.09
      = 0.91
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