Linear Algebra Answers

Let V be a subspace of R^4 and S = {u1,u2,u3} be a basis for V. Suppose v1,v2,v3 are vectors in V such that(v1)S = (1,−2,0), (v2)S =(2,−7,4),and (v3)S =(−3,8,−1).
Suppose v1 = (5,−5,0,0), v2 = (10,5,−10,−10), and v3 =(−5,0,−5,5).
Find u1, u2, and u3.

Let V be a subspace of R^4 and S = {u1,u2,u3} be a basis for V. Suppose v1,v2,v3 are vectors in V such that(v1)S = (1,−2,0), (v2)S = (2,−7,4), and (v3)S = (−3,8,−1).
Show that {v1, v2, v3} is also a basis for V.

Determine whether the set S of vectors is linear independent or not: S = {u1, u2, u3, u4} ⊆ R^4, where u1, u2, u3, u4 are all different and it is known that (1, 0, 0, 0) is not a member of

[img]https://upload.cc/i1/2020/03/13/UfFVyi.jpg[/img]



R is 4

Let V be a subspace of R^4 and S = {u1,u2,u3} be a basis for V. Suppose v1, v2, v3 are vectors in V such that (v1)S = (1,−2,0), (v2)S =(2,−7,4), and (v3)S =(−3,8,−1).
Show that {v1, v2, v3} is also a basis for V.

[img]https://upload.cc/i1/2020/03/12/Bl1aVO.jpg[/img]



R is 4

Let U,V be subspaces of Rn. Show that U ∩ V = {0} if and only if S ∪ T is a linearly independent set of vectors for every linearly independent set S = {u1,u2,...,uk} ⊆ U and every linearly independent set T = {v1,v2,...,vl} ⊆ V.

Let U, V be subspaces of R^n. Prove that U + V = {u + v : u ∈ U and v ∈ V} is also a subspace of R^n.

Determine which vectors in R^4 belong to both span{(1, −2, −2, 3), (−1, 3, 1, −2)} and span{(0, 1, 0, −1), (1, −3, 0, 0)}.

[img]https://upload.cc/i1/2020/03/11/cCgfzY.jpg[/img]



the digit number R is 4