###### Exercise 7

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.

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

A set of 4 linearly independent vectors in \(\real^4\text{.}\)

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

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

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