1.Determine by inspection why the given set S is not a basis for R^3. (That is, either S is linearly dependent or S does not span R^3 S = {u1, u5} 2.Use theorem 9, property 3 to determine whether the given set is a basis for the indicated vector space. (Theorem 9, property 3: Let W be a subspace of R^n with dim(W)=p; any set p linearly independent vectors in W is a basis for W ) S = {v1, v2, v4} for R3

1.Determine by inspection why the given set S is not a basis for R^3. (That is, either S is linearly dependent or S does not span R^3 S = {u1, u5} 2.Use theorem 9, property 3 to determine whether the given set is a basis for the indicated vector space. (Theorem 9, property 3: Let W be a subspace of R^n with dim(W)=p; any set p linearly independent vectors in W is a basis for W ) S = {v1, v2, v4} for R3

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Similar questions

Let V be an F vector space of dimension n. Prove that, for k ≤n the vectors V₁, V2, ..., Uk are linearly independent in V ⇒ v₁^₂ ^..^ Uk ‡ 0 in ^* (V) (Hint: extend basis....) Vk
Let W be the subspace spanned by Note that this basis is not orthogon Tind the orthogonal projection of -3 into W.
If W\index{1} and W\index{2} are subspace of a vector space V(F), then show that W\index{1}+W\index{2} is also a subspace of V(F).
please send correct handwritten solution for Q3
Consider the subspace H of Rª given by -2a + 2b + 4c -26 −4a + 8b+ 8c -2a + 4c H : a, b, c ER a. Find a basis for H. (Note: Use one vector per answerbox. It's okay if some of the answerboxes remain empty.) " } Why am I not getting partial credit? b. State the dimension of H. dim(H) =
suppose that x↓1,..,x↓(n-1) are linearly independent vectors in R^n and also x↓n is notin the span of x↓1,..,x↓(n-1) . 1. prove that x↓1,...,x↓n is a basis of R^n. 2. Prove that if x↓(n+1)∈R^n, then x↓1,..,x↓n,x↓n+1 are not linearly independent
Consider the subspace of the Euclidean inner product space spanned by the vectors Find an orthonormal basis of
Do the following. Considering the subspace W of R^4 , which has as its basis the set B = 2 (a) Explicitly describe the orthogonal complement W+ of W and give a basis and the dimension of this subspace; (b) Consider the following FACT from theory (theorem): If v1,v2, .. , vr is an orthogonal basis of a subspace W of R" and v €R" then the vector projection projw (v) of v onto W is given by : projw (v) = proju, (v) + projuz(v) +...+ projo, (v). It is further proven that this is the vector of W closest to the vector v. Given the result above, find the vector of W closest to 1 E R'. v = 3