###### Exercise7

Given below are some descriptions of sets of vectors that form the columns of a matrix $$A\text{.}$$ For each description, give a possible reduced row echelon form for $$A$$ or indicate why there is no set of vectors satisfying the description by stating why the required reduced row echelon matrix cannot exist.

1. A set of 4 linearly independent vectors in $$\real^5\text{.}$$

2. A set of 4 linearly independent vectors in $$\real^4\text{.}$$

3. A set of 3 vectors that span $$\real^4\text{.}$$

4. A set of 5 linearly independent vectors in $$\real^3\text{.}$$

5. A set of 5 vectors that span $$\real^4\text{.}$$

in-context