Suppose I have a basis for a subspace(adsbygoogle = window.adsbygoogle || []).push({}); Vin [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]

Vhas 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!

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# Change of basis in R^n and dimension is <n

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