Euclidean space as a vector space
Let R3 = {(x, y, z) | x, y, z ∈ R}. Then operations which can be performed in R3 are
Let A and B be the statements as given below :
A : R4 = {(a, b, c, d) | a, b, c, d ∈ R} is a vector space over R
B : R4 = {(a, b, c, d) | a, b, c, d ∈ R} is a vector space over Q
Then
A : R4 = {(a, b, c, d) | a, b, c, d ∈ R} is a vector space over R
B : R4 = {(a, b, c, d) | a, b, c, d ∈ R} is a vector space over Q
Then
We can visualize geometrically the n-dimensional Euclidean space, n ∈ N, for
Let V be a vector space over R and let A and B be the statements as given below :
A : a+b = a+c ⇒ b=c; where a, b, c ∈ V
B : α.b = α.c ⇒ b=c; where α ∈ F and b, c ∈ V
Then
A : a+b = a+c ⇒ b=c; where a, b, c ∈ V
B : α.b = α.c ⇒ b=c; where α ∈ F and b, c ∈ V
Then