V = {(a1, a2, . . ., an) : ai is an element of R for i = 1, 2, . . ., n}; and V is a vector space over R. Is V a vector space over the field of complex numbers with the operations of coordinate wise addition and scalar multiplication?

Tirimwb

Tirimwb

Answered question

2022-07-26

V = {(a1, a2, . . ., an) : ai is an element of R for i = 1, 2, . . ., n}; and V is a vector space over R. Is V a vector space over the field of complex numbers with the operations of coordinate wise addition and scalar multiplication?

Answer & Explanation

gardapati5u

gardapati5u

Beginner2022-07-27Added 9 answers

V is not a vector space over complex numbers bcasue any imaginary number multiplied by a vector in V is not in V. Hence V is not a vector space over complex numbers.

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