Question 1 (A) Let V= MATH 235 W24 - A3 -{(a): a,b € R} with addition © defined by · (9) ~ (1) − ( + d)- b+ and let F = C with multiplication © defined by a Ⓒ (a) = • (d) = (ad). product of the complex number a and the real number c. Show that (V, D, F, Ⓒ) is not a vector space. by (B) Let V= = {(i): a,b € C} with addition © defined (i) Show that (V., F, O) is a vector space. and let F = R with multiplication © defined by a Ⓒ (a) = (ad), product of the real number a and the complex number c. (ii) Show that where ac is the (9) Ⓡ (2) - (+a). = where ac is the {(1)· (;)} is linearly independent in this vector space. (iii) Find a basis for this vector space, and thus state the dimension of (V, , F, 0).

Solved: Question 1 (A) Let V= MATH 235 W24 - A3 -{(a): a,b € R} with addition

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question 1 a let v math 235 w24 a3 a a b eur r with addition c defined

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Question 1 (A) Let V= MATH 235 W24 - A3 -{(a): a,b € R} with addition © defined by · (9) ~ (1) − ( + d)- b+ and let F = C with multiplication © defined by a Ⓒ (a) = • (d) = (ad). product of the complex number a and the real number c. Show that (V, D, F, Ⓒ) is not a vector space. by (B) Let V= = {(i): a,b € C} with addi