Numerical Analysis Class/Exam2002_1

2002. 4. 23

1. For given 2 lines

y1 = m1x1 - b1

y2 = m2x1 - b2

Show that the angle @ between two lines

tan@ = (m1-m2) / (1+m1*m2)

2. Find the intersection point between the plane 3x+4y+z=24 and the line whose end points are p0=(10,-10,2), p1=(10,2,2)

(a) First. find the parametric equation for line for (t = 0 ~ 1)

(b) Find the value of the parametric variable corresponding to the intersection point.

(c) Find the values of the X,Y,Z coordinate values of plane.

3. For given pair of vectors a=3,0,-2, b=0,-1,3

(a) Compute the scalar product.

(b) Compute the angle between the vectors.

4.

(a) pivoting ��������� ���택하��� ��������� ������하������.

(b) Maximal column pivoting ���

(c) Scaled partial pivoting ��������� ������하������.

5. Lagrange, Hermite, spline 함������ �������� Smoothness ������������ ������ ������하������.

6. For given p0, p1, p0u, p1u, induce the p(u)=au^3 + bu^2 + cu + d, in the form of p(u)=U*M*B (������������ Dot Product���)

where

~cpp 
U = [u^3 u^2 u 1]

B = [p0 p1 p0u, p1u ]T

M = 
[ 2 2 1 1 ] 
[ -3 3 -2 -1 ]
[ 0 0 1 0 ]
[ 1 0 0 0 ]