Exercise 7

Given below are some descriptions of sets of vectors that form the columns of a matrix $A$. 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 $\real^5$.

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

3. A set of 3 vectors whose span is $\real^4$.

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

5. A set of 5 vectors whose span is $\real^4$.