Linear combination/(2,5,-3)/By (1,2,3), (0,1,1) and (-1,2,4)/Exercise

Write in ${}\mathbb {Q} ^{3}$ the vector

$(2,5,-3)$

as a linear combination of the vectors

$(1,2,3),(0,1,1),{\text{ and }}(-1,2,4).$

Prove that it cannot be expressed as a linear combination of two of the three vectors.

Create a solution