Question 5 1 pts Let V be a subspace of R100, and let S be a set of vectors such that V = span(S). (S is a spanning set for V.) Build a matrix A using the vectors of S as columns The dimension of V must be equivalent to all of the following EXCEPT: the rank of A the number of "leading 1s" in the RREF of A the number of vectors in S the number of nonzero rows...
2 5 Do the vectors u = and v= 3 7 span R3? -1 1 Explain! Hint: Use Let a, a2,ap be vectors in R", let A = [a1a2..ap The following statements are equivalent. 1. ai,a2,..,a, span R" = # of rows of A. 2. A has a pivot position in every row, that is, rank(A) Select one: Oa. No since rank([uv]) < 2 3=# of rows of the matrix [uv b.Yes since rank([uv]) =2 = # of columns of...
(10) Let ū ER. Show that M = {ū= | ER*:ūū= 0) is a subspace of R'. Definition: (Modified from our book from page 204.) Let V be a subspace of R". Then the set of vectors (61, 72, ..., 5x} is a basis for V if the following two conditions hold. (a) span{61, 62,...,x} = V (b) {61, 62, ..., 5x} is linearly independent. Definition: Standard Basis for R" The the set of vectors {ēi, 72, ..., en) is...
Consider a subspace V of RS that has a spanning set consisting of vectors {[:] [:] } 1 A. Find out if is an element of V B. What is the dimension of V? C. Find a linearly independent set of two vectors in V
0/1 pts Inooreat Question 9 Suppose W is a subspace of R" spanned by n nonzero orthogonal vectors. Explain why WR Two subspaces are the same when one subspace is a subset of the other subspace. Two subspaces are the same when they are spanned by the same vectors Two subspaces are the same when they are subsets of the same space Two subspaces are the same when they have the same dimension Incorrect 0/1 pts Question 10 Let U...
7. In each part of this problem a set of n vectors denoted V, , denoted V. Carefully follow these directions V, is given in a vector space i) Determine whether or not the n vectors are linearly independent. i) Determine whether or not the n vectors are a spanning set of V Then find a basis and the dimension of the subspace of V which is spanned by these n vectors. (This subspace may be V itself.) a. V...
Exercise 5 Let z and y be linearly independent vectors in R" and let S- span(,y). We can use r and y to define a matrix A by setting (a) Show that A is symmetric (b) Show that N(A) S (c) Show that the rank of A must be 2.
Exercise 5 Let z and y be linearly independent vectors in R" and let S- span(,y). We can use r and y to define a matrix A by setting (a)...
2s+2t 3s . Show that W is a subspace of R Let W be the set of all vectors of the form by finding vectors u and v such that W = Span{u,v). 3s 4t Write the vectors in W as column vectors. EHRIE 2s +2t 3s #su + tv 3s 4t
Please answer questions 2&3. Thank you!
Remember that: A subspace is never empty, and is either the just the zero vector. i.e. [0), or has an infinite number of vectors A basis for a subspace is a set of t vectors. where t is the dimension of the subspace (usually a small number.) These vectors span the subspace and are linearly independent. This means that 0 can never part of a basis. The basis of the subspace (0) is empty....
Question 5: Multiple Choices Assume that vi,2,ig are vectors in R3. Let S span ,02,s and let A be the matrix whose columns are these vectors. Assume that 1 -1 1 0 0 0-3a +b-2c We can thus conclude that A. {6,6,6) is L1. B. The point (1,1 - 1) is in the span of (o,2,s) C. The nullity of A is 2 D. The rank of A is 3 E. B and C are both correct