State with reasons, whether the following algebraic operations with scalar and vector.A Adding any two scalars.B Adding a scalar to a vector of the same dimensions.C Multiplying any vector by any scalar.D Multiplying any two scalars.E Adding any two vectors.F Adding a component of a vector to the same vector.

Let V be the set of all ordered pairs of real numbers, and consider the following vector addition and scalar multiplication operations on u = (U1, U2) and v = (V1, V2): u v = (U1 V1, U2 V2), ku = (ku1, ku2). Is there a zero vector in V? If so, what is it? For a given vector u ∈ V, is there a vector  u ∈ V such that u ( u) = 0? If so, what is it? Find all axioms, if any, from the list of 10 axioms for real vector spaces that fail to hold and prove that they are not holding.

determine whether the given set together with the specified operations of addition and scalar multiplication is a vector space if it is not select all of the axioms that fail to hold let u v 30512

30 Calculator In a scale drawing of a rectangular living roon f... | Filo

Scalars vs. Vectors | Overview, Differences & Examples

Scalar Quantity | Definition, Rules & Examples