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Assertion (A): An LTI discrete system represented by the difference equation. y (n+2)-5y(n+1)+6y(n) =x(n) is unstable. Reason (R): A system is unstable if the roots of the characteristic equation lie outside the unit circle.

Assertion (A): An LTI discrete system represented by the difference equation. y (n+2)-5y(n+1)+6y(n) =x(n) is unstable. Reason (R): A system is unstable if the roots of the characteristic equation lie outside the unit circle. Correct Answer Both A and R are true and R is the correct explanation of A

Difference equation is y (n+2)-5 y (n+1) + 6 y (n) =x (n). Taking z-transform, H (z) =1/ (z-2) (z-3). The characteristic equation has roots z =2, 3. Since, the characteristic equation has roots outside the unit circle, hence the system is unstable.

Related Questions

An assertion and a reason are given below. Assertion: The phenomenon of nuclear fission generates great energy. Reason: The process in which a nucleus is broken into two parts is called nuclear fission. Choose the answer. A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion. B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion. C. Both Assertion and Reason are false. D. Assertion is true but Reason is false.
Which of the following statements is/are true? A: If a circle is formed from a wire, which was initially in the shape of a semi-circle, then ratio of radius of circle and that of semi-circle will be 7: 11. B: If in a semi-circle of radius ‘r’, another semi-circle of radius ‘4r/5’ is drawn, then area of the remaining part of larger semi-circle will be ‘3πr2/5’. C: In a circle of radius ‘r’, if ‘O’ is the center of circle and radii OA and OB are at the angle of 45°, then the length of major arc AB will be ‘7πr/8’.
Consider the following statements in respect of the roots of the equation x3 - 8 = 0: 1. The roots are non-collinear. 2. The roots lie on a circle of unit radius. Which of the above statements is/are correct?
In a certain number system there are only two notations to represent numbers: @ and %. 0 is represented by @ and 1 by %. The subsequent numbers are represented in the following manner: 2 is represented as %@, 3 is represented as %%, 4 is represented as %@@, 5 is represented as %@% and so on. Based on this coded language, answer the following questions: What number is represented by %%@%@%%?
The following items consist of two statements, one labeled as “Assertion (A)” and the other labeled as the “Reason (R)”. You are to examine the two statements carefully and decide if the Assertion (A) and the Reason (R) are individually true and if so whether the reason is a correct explanation of the assertion. Select your answer to these items using the codes given below and mark your answer accordingly. Assertion (A): In a magnetron, each cavity with its input gap acts as an open circuit transmission line of length half wavelength long. Reason (R): In magnetrons, the usual mode employed is the ‘π’ mode, where the phase change between the adjacent cavities is π radians.
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Direction-The question have two statements.
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Assertion (A): Interest payable on working capital should be treated as an item of operating expenses.
Reason (R): Interest is the cost of capital used in the business.
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Assertion (A) Balance sheet does not reveal ownership of business.
Reason (R) Assets are just unrefined cost.