Question

the basis {(1,0,0)(0,1,0)(0,0,1)}of the vector space R³(R) is known as​

Answer 1

Answer:

?

Step-by-step explanation:

Answer 2

Normal basis

• A normal basis is a specific type of basis for Galois extensions of finite degree that forms a single orbit for the Galois group in mathematics, more especially the algebraic theory of fields.
• Any finite Galois extension of fields has a normal basis, according to the normal basis theorem.
• Galois module theory in algebraic number theory deals with the more complex issue of whether a normal integral basis exists.
• a non zero vector (p, q, r) in R3, where p, q, and r are each ≠ 0, can be expressed as a linear combination of the basis vectors:
• a = (1,0,0), b = (0,1,0) and c = (0,0,1). pa + qb + rc = (p, q, r).
• Another way to show is to prove that the set (a, b, c) is linearly independent. ==> the 3x 3 determinant formed is non-zero. The determinant = 1.

Hence, the basis {(1,0,0)(0,1,0)(0,0,1)}of the vector space R³(R) is known as​ normal basis.

#SPJ2