Show that the set V of positive real numbers with operations Addition: $x + y = xy$ Scalar Multiplication: $kx = x^k$ is a vector space where x, y are any two real numbers and k is any scalar.

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written 7.9 years ago by

teamques10 ★ 65k

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engineering mathematics

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written 7.9 years ago by

teamques10 ★ 65k

Axioms of vector spaces:

Closure Axioms (C)
Addition Axioms (A)
Scalar Multiplication Axioms (S)

1. Closure (C)

$C_{1}$: Since x + y = xy and x, y are real numbers

$\therefore$ V is closed under addition.

$C_{2}$: Since $kx = x^k$, where k is given as any scalar. …

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written 2.4 years ago by

teamques10 ★ 65k

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Huihuihui mazaakk kar rahi thii , upper wale aadmi ne ghalat kara hai .. ye vector space form nahi kar rha :)

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