A First Course in Linear Algebra · Problem SS.T10

Vectors — Robert Beezer

Mathematics — Linear Algebra · spanning-sets-proofs

Problem

Suppose that v1,v2∈Cm\mathbf{v}_1, \mathbf{v}_2 \in \mathbb{C}^m. Prove that ⟨{v1,v2}⟩=⟨{v1,v2,5v1+3v2}⟩\langle\{\mathbf{v}_1, \mathbf{v}_2\}\rangle = \langle\{\mathbf{v}_1, \mathbf{v}_2, 5\mathbf{v}_1 + 3\mathbf{v}_2\}\rangle

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