Exercise 1:

Shaded portion is --Select-- Range R(𝑇) Nullspace N(𝑇) 𝑊 𝑉 Submit

Exercise 2:

Shaded portion in domain is --Select-- Range R(𝑇) Nullspace N(𝑇) 𝑊 𝑉

Submit

Shaded portion in co-domain is --Select-- Range R(𝑇) Nullspace N(𝑇) 𝑊 𝑉

Submit

Exercise 3:

Consider the linear transformation T: R² → R² defined by

 T(x, y) = (x, 2x); x, y ∈ R²

Null Space ≡ N(T) = {(0, y) : y =0 =-1 =2 ∈𝑅 } Submit

Nullity T = 0 1 -1 2 -2 Submit

Range ≡ R(T) = {(x, 𝑥+2 𝑥² 2𝑥 𝑥-2 ) : x ∈ R}Submit

Rank T = 0 1 -1 2 -2 Submit

Exercise 4:

What will be the rank of the matrix of T w.r.t. the standard bases?

  Answer: /