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IniquiTrance
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Suppose I have a basis for a subspace V in [tex]\mathbb{R}^{4}[/tex]:
[tex]\mathbf{v_{1}}=[1, 3, 5, 7]^{T}[/tex]
[tex]\mathbf{v_{2}}=[2, 4, 6, 8]^{T}[/tex]
[tex]\mathbf{v_{3}}=[3, 3, 4, 4]^{T}[/tex]
V has dimension 3, but is in [tex]\mathbb{R}^{4}[/tex]. How would one switch basis for this subspace, when you can't use an invertible transition matrix?
Thanks!
[tex]\mathbf{v_{1}}=[1, 3, 5, 7]^{T}[/tex]
[tex]\mathbf{v_{2}}=[2, 4, 6, 8]^{T}[/tex]
[tex]\mathbf{v_{3}}=[3, 3, 4, 4]^{T}[/tex]
V has dimension 3, but is in [tex]\mathbb{R}^{4}[/tex]. How would one switch basis for this subspace, when you can't use an invertible transition matrix?
Thanks!