Only one option is correct. Being u,v and w linearly dependent vectors of a linear space...

Question

Question

Only one option is correct.

Being u,v and w linearly dependent vectors of a linear space E.

Then :

a) u and v are linearly independent .

b) u and v are linearly dependent .

c) u, u + v and u + w are linearly independent .

d) u, u + v and u + w are linearly dependent .

Answer 1

Answer #1

Answer 2

Similar Homework Help Questions

Let u = and v= Determine whether the vectors u and v are linearly independent or...

Let u = and v= Determine whether the vectors u and v are linearly independent or linearly dependent, and choose the most correct answer below. A. The vectors are linearly independent. B. We cannot easily tell whether the vectors are linearly independent or linearly dependent. C. The vectors are linearly dependent.
linear alegbra Let u, v, w be linearly independent vectors in R3. Which statement is false?...

linear alegbra Let u, v, w be linearly independent vectors in R3. Which statement is false? (A) The vector u+v+2w is in span(u + u, w). (B) The zero vector is in span(u, v, w) (C) The vectors u, v, w span R3. (D) The vector w is in span(u, v).
please help with this linear algebra question Question 10 [10 points] Let V be a vector...

please help with this linear algebra question Question 10 [10 points] Let V be a vector space and suppose that {u, v, w is an independent set of vectors in V. For each of the following sets of vectors, determine whether it is linearly independent or linearly dependent. If it is dependent, give a non-trivial linear combination of the vectors yielding the zero vector. a) {-v-3w, 2u+w, -u-2v} is linearly independent b) {-3v-3w, -u-w, -3u+3v} < Select an answer >

2) Given 3 vectors. 11 | u = 0 | u = -1 L2 a) What...

2) Given 3 vectors. 11 | u = 0 | u = -1 L2 a) What vector space do these vectors belong to? b) Geometrically describe the space spanned by vectors uj and u2. c) Is vector, v, in the subspace spanned by the vectors uj and u2? d) Are all 3 vectors linearly dependent or independent of each other? Explain why or why not. e) If possible, find the linear combination of vectors u; and uz that equals vector...
6. Are vectors ū= (1,-1,2 %; v = (-1,-1,-1) and W = (-1,-5,1 ) linearly dependent?...

6. Are vectors ū= (1,-1,2 %; v = (-1,-1,-1) and W = (-1,-5,1 ) linearly dependent? If they are, write ü as a linear combination of vectors v and w.
1. Suppose u, V, and w is a linearly independent set (these would have to be...

1. Suppose u, V, and w is a linearly independent set (these would have to be non-zero vectors). a. Ifa- u conclusion. v and b-v+ w, is the set (a, b, w] linearly independent? Show the work needed to reach the d b v+ w is the set (a. b,w) linearly independent? Show the work needed to reach the conclustion b. Ifa w v and

Given the following vectors u and v, find a vector w in R4 so that {u,...

Given the following vectors u and v, find a vector w in R4 so that {u, v, w} is linearly independent and a non- zero vector z in R4 so that {u, v, z} is linearly dependent: 1-3 8 -8 -2 u = V= 5 -4 10 0 w=0 1- z=0 0
Q4. Let T :V + W be a one-to-one linear transformation (i.e. an equation T(u) =...

Q4. Let T :V + W be a one-to-one linear transformation (i.e. an equation T(u) = T(v) always implies u = v). (a) Show that the kernel of T contains only the zero vector. (b) Show that if the set {T(v1), ...,T(un)} is linearly dependent, then the set {V1, ..., Un} is linearly dependent as well. Hint: use part (a).
Q4. Let T :V + W be a one-to-one linear transformation (i.e. an equation T(u) =...

Q4. Let T :V + W be a one-to-one linear transformation (i.e. an equation T(u) = T(v) always implies u = v). (a) Show that the kernel of T contains only the zero vector. (b) Show that if the set {T(v1),...,T(Un)} is linearly dependent, then the set {01, ..., Un} is linearly dependent as well. Hint: use part (a).

Q4. Let T :V + W be a one-to-one linear transformation (i.e. an equation T(u) =...

Q4. Let T :V + W be a one-to-one linear transformation (i.e. an equation T(u) = T(v) always implies u = v). (a) Show that the kernel of T contains only the zero vector. (b) Show that if the set {T(v1),...,T(Un)} is linearly dependent, then the set {01, ..., Un} is linearly dependent as well. Hint: use part (a).