Abstract Algebra Answers

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

(10x^3+27x^2+14x+5) divided by (x^2+2x)

Identify the independent and dependent variables. Write a rule in funtion notation for each situation.

an automatic pouring machine is filling cans of liquid condenced milk of weight 32 oz. with SD 0.4. Due to defect in the machine some cans contain 31.50 oz. If 1000 such cans of condensed milk are imported, how many cans contain less amount of milk?