Kunze Linear Algebra · Problem 3.4.5

Linear Transformations

Mathematics — Methods · range-null-space-from-matrix

Problem

Let

T

be the linear operator on

R^3

, the matrix of which in the standard ordered basis is

A = \begin{bmatrix} 1 & 2 & 1 \\ 0 & 1 & 1 \\ -1 & 3 & 4 \end{bmatrix}.

Find a basis for the range of

T

and a basis for the null space of

T