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If a vector space $$ has a basis consisting of 5 vectors then for $$,
$$ is linearly dependent. $$ is linearly independent.
If a vector space $$ has a basis consisting of 5 vectors then for $$,
$$ spans $$. $$ does not span $$.

Determine the dimensions of $$ and $$.

$$

$$

Determine the dimensions of $$ and $$.

$$

$$

Determine the dimensions of $$ and $$.

$$

$$

Determine the dimensions of $$ and $$.

$$

$$

True/False: A plane in $$ is a two dimensional subspace of $$
True False
A plane in $$ that doesn’t intersect the origin is not a subspace, so couldn’t be a subspace of dimension 2.

True/False: If $$ and $$ is a linearly independent set with $$ vectors, then $$ is a basis fo $$.
True False