LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – MATHEMATICS
SECOND SEMESTER – APRIL 2012
MT 2100 – MATHEMATICS FOR COMPUTER SCIENCE
Date : 23-04-2012 Dept. No. Max. : 100 Marks
Time : 9:00 – 12:00
PART A
Answer ALL the questions: 10×2 = 20
- Define symmetric matrix with an example.
- Prove that.
- Remove the fractional coefficients from the equation
- Find the partial differential coefficients of .
- Evaluate.
- Evaluate
- Solve the equation = 0.
- Derive the partial differential equation by eliminating the arbitrary constants from .
- Find an iterative formula to , where N is a positive integer.
- Write Simpson’s
PART B
Answer any FIVE questions: 5×8 = 40
- Show that the equations are consistent and solve them.
- Prove that
- Find the condition that the roots of the equation may be in geometric progression.
- Integrate with respect to x.
- (i) Evaluate
(ii) Prove that (4 + 4)
- Solve the equation
- Solve (i) (ii) (4 + 4)
- Determine the root of correct to three decimals using, Regula Falsi method.
PART C
Answer any TWO questions: 2×20 = 40
- (i) Find all the characteristic roots and the associated characteristic vectors of the matrix
A =.
(ii) If then prove that (14+6)
- (i) Solve the equation
(ii) If , prove that . (14+6)
- (i) Integrate with respect to x.
(ii) Solve (6+14)
- (i) Solve
(ii) Evaluate using trapezoidal rule and Simpson’s rule. (8+12)
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