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(Solved by Expert Tutors) Exercise 3.1.1 Suppose you have R2 and the + operation is as follows:(a

+ (c,d) = (a+d,b+c).Scalar multiplication is defined in the usual way. Is this a vector space? Explain why or why not.

Exercise 3.1.2 Suppose you have R2 and the + operation is defined as follows.(a,b) + (c,d) = (0,b+d)Scalar multiplication is defined in the usual way. Is this a vector space? Explain why or why not.

Exercise 3.1.3 Suppose you have R2 and scalar multiplication is defined as c(a,b) = (a, cb) while vectoraddition is defined as usual. Is this a vector space? Explain why or why not.

Exercise 3.1.4 Suppose you have R2 and the + operation is defined as follows.(a,b) + (c,d) = (a?c,b?d)Scalar multiplication is same as usual. Is this a vector space? Explain why or why not

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