MathAlgebraLinear algebraLinear operators

Intersection and sums of subspaces

Functions are not easy

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Let's look at the set $F$ of functions from $\mathbb{R}$ into $\mathbb{R}$ .

In this vector space, we can find the set $Z$ of functions $f$ such that $f(0)=0$ and the set $N$ of functions that $f(x)\neq 0$ for all $x$ .

Select the true statement.

HINT: For any function $f$ , we have that $f(x) - f(x)=0$

Select one option from the list

F = Z + N

F = Z \bigoplus N

F = Z \cap N

N

is not a subspace of

F

F = Z \cup N

Z

is not a subspace of

F

dim(F) = dim(Z) + dim(N)

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