Manakah di antara berikut ini yang merupakan definisi yang benar tentang ruang vektor?Which of the following is the correct definition of a vector space?AHimpunan vektor yang tidak memenuhi semua aksioma ruang vektor.A set of vectors that does not satisfy all the axioms of a vector space.BHimpunan vektor yang memenuhi beberapa aksioma ruang vektor.A set of vectors that satisfies several axioms of a vector space.CHimpunan vektor yang memenuhi semua aksioma ruang vektor.A set of vectors that satisfies all the axioms of a vector space.DHimpunan vektor yang terdiri dari hanya satu elemen.A set of vectors consisting of only one element.
Question
Manakah di antara berikut ini yang merupakan definisi yang benar tentang ruang vektor?Which of the following is the correct definition of a vector space?AHimpunan vektor yang tidak memenuhi semua aksioma ruang vektor.A set of vectors that does not satisfy all the axioms of a vector space.BHimpunan vektor yang memenuhi beberapa aksioma ruang vektor.A set of vectors that satisfies several axioms of a vector space.CHimpunan vektor yang memenuhi semua aksioma ruang vektor.A set of vectors that satisfies all the axioms of a vector space.DHimpunan vektor yang terdiri dari hanya satu elemen.A set of vectors consisting of only one element.
Solution
To determine the correct definition of a vector space, let's analyze each option step by step:
A. "A set of vectors that does not satisfy all the axioms of a vector space."
- This option is incorrect because a vector space must satisfy all the axioms of a vector space.
B. "A set of vectors that satisfies several axioms of a vector space."
- This option is also incorrect because satisfying only several axioms is not sufficient. A vector space must satisfy all the axioms.
C. "A set of vectors that satisfies all the axioms of a vector space."
- This option is correct. A vector space is defined as a set of vectors that satisfies all the axioms of a vector space, including closure under addition and scalar multiplication, the existence of a zero vector, and others.
D. "A set of vectors consisting of only one element."
- This option is incorrect because a vector space is not defined by the number of elements it contains but by whether it satisfies all the axioms of a vector space. A vector space can have one element (the zero vector), but this is not a defining characteristic.
Therefore, the correct definition of a vector space is:
C. "A set of vectors that satisfies all the axioms of a vector space."
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