Null Space of Linear Transformation

Range of Linear Transformation

Example:

T: R² → R²

T(x, y) = (x, 2x); x, y ∈ R²

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

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Nullity T = 0 1 -1 2 -2

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

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Rank T = 0 1 -1 2 -2

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• Question: What will be the rank of the matrix of this linear transformation w.r.t. the standard bases?

  Answer: /