Find a basis of the subspace R4 consisting of all vectors

Question

Find a basis of the subspace of R⁴ consisting of all vectors of the form [x1, -2x1+x2, -9x1+4x2, -5x1-7x2]

 

Answer 1

[x₁, -2x₁ + x₂, -9x₁ + 4x₂, -5x₁ - 7x₂] = [1, -2, -9, -5]x₁ + [0, 1, 4, -7]x₂

 

 

A basis of the subspace is {[1, -2, -9, -5], [0, 1, 4, -7]}.