Give an example that meets these expectations Three vectors

Give an example that meets these expectations: Three vectors u₁, u₂, and u₃ in R⁴ that span the set of all vectors of the form v = (0, v2, v3, v4).

Solution

The vectors u₁ = ( 0 , 1 , 0 , 0 ) , u₂ =( 0 , 0 , 1 , 0 ) and u₃ = ( 0 , 0 , 0 0 , 1 ) spans a set of vectors of the form

( 0 , v₂ , v₃ , v₄ )

For , ( 0 , v₂ , v₃ , v₄ ) =v₂ ( 0 , 1 , 0 , 0 ) +v₃( 0 , 0 , 1 , 0 ) + v₄ ( 0 , 0 , 0 0 , 1 )

₌ v₂u₁ + v₃u₂ + v₄u₃