Linear system/Basis completion/1/Exercise

We consider the linear equations

$9x-8y+7z-8u+4v=0,$

$3y+7z-4u+6v=0,$

$-2z+5u+7v=0,$

over $ℝ$.

1. Determine a basis ${𝔟}_1$ of the solution space of this linear system.
2. Extend the basis ${𝔟}_1$ to a basis ${𝔟}_2$ of the solution space of the linear system consisting of the first two equations.
3. Extend the basis ${𝔟}_2$ to a basis ${𝔟}_3$ of the solution space of the linear system consisting of the first equation alone.
4. Extend the basis ${𝔟}_3$ to a basis ${𝔟}_4$ of the total space ${ℝ}^5$.

Create a solution