Linear map equation and its solution

Consider the linear transformation T: R2→R2 defined by T(x, y)=(x, 0), where x, y∈R. Then range of T is
Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Consider the linear transformation T: R3→R2 defined by T(x, y, z)=(x, y+z), where x, y, z∈R. Then range of T is
Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Consider the linear transformation T:R2→R2 defined by T(x, y)=(x, -y), where x, y∈R. Then
Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Consider the linear transformation T:R3→R2 defined by T(x, y, z)=(x+y+z, 0), where x, y, z∈R. Then
Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Consider the map T:R2→R3 such that T(1, 3)=(1, 0, 0), T(2, 6)=(2, 0, 0), T(1, 1)=(0, 1, 0) and T(2, 4)=(1, 1, 0). Then T is
Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Consider the map T:R2→R2 and S:R2→R2 such that T(2, 1)=(1, 1), T(1, 2)=(1, 1), S(4, 2)=(3, 3) and S(8, 4)=(5, 6). Let the statements A and B be as given below: A: T is one-to-one. B: S is not linear. Then which of following holds
Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation