Let W be the subspace of R^(4) spanned by vectors (1,-2,5,3)^(T),
(2,3,1,-4)^(T), (3,8,-3,-5)^(T). Extend the basis of W to a basis of the whole space of R^(4).
Let W be the subspace of R^(4) spanned by vectors (1,-2,5,3)^(T),
(2,3,1,-4)^(T), (3,8,-3,-5)^(T). Extend the basis of W to a basis of the whole space of R^(4).
Well, if W has 3 basis vectors, then it must define a hyperplane of $\displaystyle \mathbb{R}^4$. Thus use the dot product to find a vector in $\displaystyle \mathbb{R}^4$ that is perpendicular to each of the basis vectors of W.