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