GATE | GATE-IT-2004 | Question 32
Let A be an Let A be an n × n matrix of the following form.
What is the value of the determinant of A?
The first thing you need to get by seeing these type of questions is:- Go for substitution method. For n=2, the values will be A) 16 B) 26 C) 7 D) 8 As all the values are unique for a small value of n, it does not take much time. The given matrix will be A = [3 1] [1 3] So, det(A) = 3*3-1*1 = 8 Option (D) is the answer.
Alternative method:- You can frame the relations in between det(An+1), det(An), det(An-1) i.e. d(An+1) = 3*d(An) - d(An-1) X = 3*X^0 - X^-1 X^2 = 3*x - 1 Solution for this equation is (3+sqrt(5))/2, (3-sqrt(5))/2 The only option which has roots of type (3+sqrt(5)) is D. From this, you can match the options easily.
This explanation has been provided by Anil Saikrishna.
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