Linear system/Dimension/2/Exercise

a) Determine the dimension of the solution space of the linear system

${}2x+5y+7z+4u-3v+2w=0\,$

${}4x+9y+6z+5u-v+w=0\,$

${}7x+8y-3z+u+3v+3w=0\,$

${}-x+6y+16z+8u-7v=0\,$

in the variables ${}x,y,z,u,v,w$.

b) What is the dimension of the solution space if we consider the system in the variables ${}x,y,z,u,v,w,r,s$?

Create a solution