# Answer to Question #21411 in Abstract Algebra for werty

Question #21411

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)

(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)

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