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Vectors — Robert Beezer
Mathematics — Linear Algebra · spanning-sets
Problem Let u = [ 1 3 − 2 ] \mathbf{u} = \begin{bmatrix} 1 \\ 3 \\ -2 \end{bmatrix} u = 1 3 − 2 v = [ 2 − 2 1 ] \mathbf{v} = \begin{bmatrix} 2 \\ -2 \\ 1 \end{bmatrix} v = 2 − 2 1 w 1 \mathbf{w}_1 w 1 u \mathbf{u} u v \mathbf{v} v ⟨ { u , v , w 1 } ⟩ = ⟨ { u , v } ⟩ \langle\{\mathbf{u}, \mathbf{v}, \mathbf{w}_1\}\rangle = \langle\{\mathbf{u}, \mathbf{v}\}\rangle ⟨{ u , v , w 1 }⟩ = ⟨{ u , v }⟩ w 2 \mathbf{w}_2 w 2 ⟨ { u , v , w 2 } ⟩ ≠ ⟨ { u , v } ⟩ \langle\{\mathbf{u}, \mathbf{v}, \mathbf{w}_2\}\rangle \ne \langle\{\mathbf{u}, \mathbf{v}\}\rangle ⟨{ u , v , w 2 }⟩ = ⟨{ u , v }⟩ Browse the problem library