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- (1) Just use the results in section 3.2 of the notes.
- (2a) A set of vectors are linearly independent if and only if there exists no real numbers such that
(2b) Equation (3) in the assignment will give you four linear equations for the four components of , which you should be able to solve very easily.
(2c) Having got the components of , it is easy to find the value of .
(2d) This problem is similar to part (2a).
- (3) Assume that and . Then evaluate and . You should get different results.
- (4a) Just use the definitions in section 3.3 and 3.4 of the lecture notes.
(4b) Compare how and transform.
(4c) No hint here!!
- (5) Just use the definitions of symmetric and anti- symmetric tensors in section 3.3 of the notes and juggle the indices!
- (6) A chocolate bar will go to the first person who presents me a perfect solution!!