A First Course in Linear Algebra · Problem SLT-C27

Linear Transformations — Robert Beezer

Mathematics — Linear Algebra · range-surjective-linear-transformations

Problem

Let T:C3→C4T: \mathbb{C}^3 \to \mathbb{C}^4 be given by T([abc])=[a+b−ca−b+c−a+b+ca+b+c]T\left(\begin{bmatrix} a \\ b \\ c \end{bmatrix}\right) = \begin{bmatrix} a+b-c \\ a-b+c \\ -a+b+c \\ a+b+c \end{bmatrix}. Find a basis of R(T)\mathcal{R}(T). Is TT surjective?

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