# linear algebra

posted by .

which of the following sets of vectors span R^3?
a.){(1, -1, 2), (0, 1, 1)}
b.) {1, 2, -1), (6, ,3, 0), (4, -1, 2), (2, -5, 4)}
c.) {(2, 2, 3), (-1, -2, 1), (0, 1, 0)}
d.) {(1, 0, 0), (0, 1, 0), (0, 0, 1), (1, 1, 1)}

can someone show the steps to check for one of them and i will try to do the rest.

Put the vectors as rows or columns in a matrix and do Gaussian Elimination (note that row rank = column rank).

You don't have to do this for a) because you can't span R^3 with two vectors. Also, it is clear that the vectors listed in d) span R^3

In case of b) after Gaussian Elimination, you should find that the rank of the matrix is 2. This means that te four vectors span a two dimensional subspace of R^3 (the reduced matrix indicates exactly what subpace)

In case of c) you should find that the rank is 3, so the three listed vectors span R^3.

• linear algebra -

i need help

## Respond to this Question

 First Name School Subject Your Answer

## Similar Questions

1. ### linear algebra

Determine whether {v1, v2, v3} is a basis for R3 v1 = [1] [-3] [1] v2 = [-3] [8] [4] v3 = [2] [-2] [2] Put the vectors as rows or columns in a matrix and perform Gaussian reduction to determne the row or column rank. In this case you …
2. ### Linear Algebra

Hello ! i try to solve Linear algebra 2 questions(but need them be written properly as mathmatical proofs) Having A matrice nXn: 1)proove that if A^2=0 the columns of matrice A are vectors in solution space of the system Ax=0 (x and …
3. ### Span linear

hello everyone!i'm breaking my head and desperate how to do it... If i have a vector in linear space V:r v1,v2.....vk,a,b having A={v1,v2.....vk,a} B={v1,v2....vk,b} C={v1,v2...vk} and its known that V=sp(A) and b∉sp(C)........ …
4. ### Calculus

Name two sets of vectors that could be used to span a set in R^3. Show how the vectors (-1,2,0) and (3,4,0) could each be written as a linear combination of the vectors you have chosen.
5. ### college Algebra/Linear Algebra

Find a Basis for each of these substances of R^4 (a) All vectors whose components are equal (b) All vectors whose component add to zero (c) All vectors that are perpendicular to (1,1,0,0) and (1,0,11) (d) The column space (In R^2) …
6. ### Linear Algebra

Let v1= (1,1,2,1) v2= (0,1,3,3) v3= (1,-1,-4,-5) v4= (1,0,-2,-4) a) Let U=span{v1,v2,v3,v4}. Find the dimension of U b) Is span {v1,v2,v3,v4}=R4?
7. ### Calculus

What does it mean to span in R2? I have this question: Which of the following sets if vectors span R2?
8. ### Linear Algebra

Let v1 = (1, 0, −1) v2 = (0, 2, 2) v3 = (−3, 4, 7) and let W = Span{v1, v2, v3}. 1. Show that v3 is a linear combination c1v1 + c2v2 of v1 and v2 by finding the constants c1 and c2. 2. Show that W = Span{v1, v2}. 3. Show that v1 …
9. ### Linear Algebra

Let v1 = (1, 0, −1) v2 = (0, 2, 2) v3 = (−3, 4, 7) and let W = Span{v1, v2, v3}. Show that W = Span{v1, v2}?
10. ### Algebra

Let U and V be the points with position vectors u = (1, 2, −1, −2) and v = (0,3,−2,2,). Find the distance from U to the span(v

More Similar Questions