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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