Which one is not a vector space?

Most sets of n-vectors are not vector spaces. P:={(ab)|a,b≥0} is not a vector space because the set fails (⋅i) since (11)∈P but −2(11)=(−2−2)∉P.

What of the following is not a vector?

Answer: Speed is not a vector quantity. It has only magnitude and no direction and hence it is a scalar quantity.

Is R2 a vector space?

The vector space R2 is represented by the usual xy plane. Each vector v in R2 has two components. The word “space” asks us to think of all those vectors—the whole plane. Each vector gives the x and y coordinates of a point in the plane : v D .

Why Z is not a vector space?

If V is a vector space over a field of positive characteristic, then as an abelian group, every element of V has finite order. If V is a vector space over a field of characteristic 0, then as an abelian group, V is divisible. The abelian group Z has neither of these properties.

Which are vector spaces?

A vector space or a linear space is a group of objects called vectors, added collectively and multiplied (“scaled”) by numbers, called scalars. Scalars are usually considered to be real numbers. But there are few cases of scalar multiplication by rational numbers, complex numbers, etc. with vector spaces.

Proving Something's NOT a Vector Space

Which of the following is not a vector space R C?

For example, R is not a vector space over C, because multiplication of a real number and a complex number is not necessarily a real number.

Which set is an example of vector space?

The simplest example of a vector space is the trivial one: {0}, which contains only the zero vector (see the third axiom in the Vector space article). Both vector addition and scalar multiplication are trivial. A basis for this vector space is the empty set, so that {0} is the 0-dimensional vector space over F.

Is R Q a vector space?

We've just noted that R as a vector space over Q contains a set of linearly independent vectors of size n + 1, for any positive integer n. Hence R cannot have finite dimension as a vector space over Q. That is, R has infinite dimension as a vector space over Q.

Is RA vector space?

R is a vector space where vector addition is addition and where scalar multiplication is multiplication.

Is RA vector space over Z?

You can't have a vector space over Z. By definition, a vector space is required to be over a field.

Is m5 6 a vector space?

This set is not a vector space. It fails the following axioms; commutative property, additive identity and distributive property B. This set is not a vector space. It fails the following axioms: multiplicative identity, associative property, distributive property additive identity C.

Which of the following is not an example of vector field?

Mass is never an example of a vector quantity.

Mass is always a scalar quantity since it only indicates the amount of matter contained in an object or body. It does not give any information regarding the direction of that body or object. Vector is associated with both the magnitude and direction.

Which of the following is not a vector product of two vector?

<br> Reason: If the product of two vectors is a vector quantity, then product is called a dot product. The result of scalar product and the vector product of two given vectors is zero .

Is R over ZP a vector space?

With the usual addition, R cannot be a vector space over Z/pZ, because every vector space over this field is a torsion group, precisely an elementary abelian p-group, that is, a direct sum of copies of Z/pZ.

Is a field a vector space?

The main difference in idea, put vaguely, is that fields are made of 'numbers' and vector spaces are made of 'collections of numbers' (vectors). You can multiply any two numbers together, and you can also take a collection of numbers and multiple them all with the same fixed number. The complex numbers form a field.

Which of the following is not an example of vector quantity *?

Kinetic energy is not a vector, since it has no direction associated with it.

What are the examples of vector field?

Examples of vector fields: Gravitational force field, electrostatic force field, fluid flowing to a river, wind is blowing. Assume that these are on 3D space.

What are some examples of vector quantity?

Are rational numbers a vector space?

So, yes, the rational numbers are a vector space over Q. Every field is a vector space over itself of dimension one.

Are numbers vectors?

Since R is a vector space over itself, real numbers are both vectors and scalars in this context. In other contexts, a real number might be a vector but not a scalar (e.g. the vector √2 in R over Q), a scalar but not a vector (e.g. the scalar 1 in R2 over R), or neither a vector nor a scalar.

Is Z7 a vector space over Z5?

@egreg we know that if F is a subfield of V then V is a vector space over F. However I see some solutions taking this the wrong and say that since Z5 is not the subfield of Z7 and concluding Z7 is not a vector space.