A First Course in Linear Algebra · Problem SLT-C26

Linear Transformations — Robert Beezer

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

Problem

Let T:C3→C3T: \mathbb{C}^3 \to \mathbb{C}^3 be given by T([abc])=[a+b+2c2ca+b+c]T\left(\begin{bmatrix} a \\ b \\ c \end{bmatrix}\right) = \begin{bmatrix} a + b + 2c \\ 2c \\ a + b + c \end{bmatrix}. Find a basis of R(T)\mathcal{R}(T). Is TT surjective?

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