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True or False: A basis of R2[x] can be extended to a basis of R3[x].

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asked 2021-06-05
True or False: A basis of R2[x] can be extended to a basis of R3[x].

Answers (1)

2021-06-06
True, As every element of R2[x] is also an element of R2[x] and so a basis of R2[x] is a lineary independent subset of R3[x]. Accordint to extension theorem, any non empty subset of vector space can be extended to a basis of that space. Hence, a basis of R2[x] can be extended to basis of R3[x]
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