A First Course in Linear Algebra · Problem SLT-C25

Linear Transformations — Robert Beezer

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

Problem

Define the linear transformation T:C3→C2,T([x1x2x3])=[2x1−x2+5x3−4x1+2x2−10x3]T: \mathbb{C}^3 \to \mathbb{C}^2, \quad T\left(\begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix}\right) = \begin{bmatrix} 2x_1 - x_2 + 5x_3 \\ -4x_1 + 2x_2 - 10x_3 \end{bmatrix} Find a basis for the range of TT, R(T)\mathcal{R}(T). Is TT surjective?

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