At least one of the answers above is NOT correct. Are the following statements true or false? 1. If the set of vectors $U$ is linearly independent in a subspace $S$ then vectors can be added to $U$ to create a basis for $S$ 2. If $S = span {u_{1}, u_{2}, u_{3}}$ , then $dim (S) = 3$ 3. If $S_{1}$ and $S_{2}$ are subspaces of $R^{n}$ of the same dimension, then $S_{1} = S_{2}$ . 4. If the set of vectors $U$ spans a subspace $S$ , then vectors can be removed from $U$ to create a basis for $S$ 5. Three nonzero vectors that lie in a plane in $R^{3}$ might form a basis for $R^{3}$ .

Question

At least one of the answers above is NOT correct. Are the following statements true or false? 1. If the set of vectors

U

is linearly independent in a subspace

S

then vectors can be added to

U

to create a basis for

S

2. If

S = span {u_{1}, u_{2}, u_{3}}

, then

dim (S) = 3

3. If

S_{1}

and

S_{2}

are subspaces of

R^{n}

of the same dimension, then

S_{1} = S_{2}

. 4. If the set of vectors

U

spans a subspace

S

, then vectors can be removed from

U

to create a basis for

S

5. Three nonzero vectors that lie in a plane in

R^{3}

might form a basis for

R^{3}

.

Accepted Answer

Expert Answer to -  At least one of the answers above is NOT correct. Are the following statements true or false? 1. If

Answer

Solution for -  At least one of the answers above is NOT correct. Are the following statements true or false? 1. If

Answer

This an additional answer to -  At least one of the answers above is NOT correct. Are the following statements true or false? 1. If

(Solved): At least one of the answers above is NOT correct. Are the following statements true or false? 1. If ...