Exercise 2A Problem 12

Linear Algebra Done Right - Exercise 2A Problem 12 - Solution

June 25, 2022 · 1 min · 49 words · Me | Suggest Changes

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Problem

Explain why there does not exist a list of six polynomials that is linearly independent in $\mathcal{P}_4(\mathbb{F})$

Solution

The list $1,z,z^2,z^3,z^4$ has five linearly independent elements and spans $\mathcal{P}_4(\mathbb{F})$, therefore by theorem $2.23$ no list with more than 5 elements that spans the space can be linearly independent.

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