A First Course in Linear Algebra · Problem ILT-C27

Linear Transformations — Robert Beezer

Mathematics — Linear Algebra · kernel-injective-linear-transformations

Problem

Let T:C3→C3T: \mathbb{C}^3 \to \mathbb{C}^3 be given by T([xyz])=[2x+y+zx−y+2zx+2y−z]T\left(\begin{bmatrix} x \\ y \\ z \end{bmatrix}\right) = \begin{bmatrix} 2x + y + z \\ x - y + 2z \\ x + 2y - z \end{bmatrix}. Find K(T)\mathcal{K}(T). Is TT injective?

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