Abstract Algebra Answers

A car is traveling 60 mph A bike is seen 100 yards away going 20 mph. First case is the bike is traveling in the same direction as the car; second case is that the bike is moving towards the car. The question is what is the difference in time of "closure"? (Ie., when do they arrive at the same point? What is the point(time and distance) where they would collide? Also HOW do you solve this. And is the answer for other speeds and distances linear?

40+40x0+1=

1. Given the zero-one matrices A = and B = .
(i) Find the join of A and B.
(2 marks)
(ii) Find the Boolean product of A and B.
(2 marks)

2. Given A = and B = . Find the matrix ATB.
(3 marks)

3. Given two vectors v = – 2i + 6j and w = 4i + 2j.

(i) Find the dot product .
(2 marks)
(ii) Determine whether the vectors v and w are orthogonal.
(1 mark)
(iii) Decompose v into two vectors v1 and v2 where v1 is parallel to w and v2 is orthogonal to w.
(5 marks)

4. Decompose v into two vectors v1 and v2 where v1 is parallel to w and v2 is orthogonal to w.
v = 3i – 4j , w = i – j
(6 marks)

5. Find each of the following quantities if v = 6i – 2j and w = 8i + 6j.

(i) 2v + 3w
(2 marks)
(ii)
(1 mark)
6. Given two vectors v = ai – 6j and w = – 4i – 2j.

(i) Find the dot product .
(2 marks)
(ii) Find the value of a so that the vectors v and w are orthogonal.
(2 marks)

show that the area of the triangle formed by the points (x1,y1,z1),(x2,y2,z2) and the origin is
1/2sqrt((y1z2-y2z1)2+(z1x2-z2x1)2+(x1y2-x2y1)2)

Water tank cylinder with 1.8m diameter and 3.1 m length put on horizontal position I need formula to the volume of water at different heights
Regards

If a group G has only three elements, show that it must be abelian.

5(2m+3)/2-(1-2m)/3=2 [3(3+2m)-(3-m)]

3x+3=3x-5