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Question 5 Let V be a subspace of R100, and let S be a set of...
Question 5 Let V be a subspace of R100, and let S be a set of vectors such that y = = 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 number of nonzero rows in a REF of A the number of vectors in S the rank of A O the number of "leading 1s"...
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...
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...
0/1 pts Inooreat Question 9 Suppose W is a subspace of R" spanned by n nonzero...
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...
(10) Let ū ER. Show that M = {ū= | ER*:ūū= 0) is a subspace 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...
solve the linear algebra question 1. (6 points) Let S be a subspace of R3 spanned...
solve the linear algebra question
1. (6 points) Let S be a subspace of R3 spanned by the columns of the matrix [1 2 0 1 1] 2 4 1 1 0 3 6 1 2 1 Find a basis of S. What is the dimension of S?
3. (15 pts) Let A be an m x n matrix with rank r, and let...
3. (15 pts) Let A be an m x n matrix with rank r, and let V = C(A). (a) V CIRP for what p? (b) What is V. in terms of a fundamental subspace for A? (c) How many vectors are in a basis for V, and how many in a basis for v 1? (d) For what m, n, and r docs Ax=b have a solution for every b? (e) Is a set of r vectors in V...
Question 5: Multiple Choices Assume that vi,2,ig are vectors in R3. Let S span ,02,s and...
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
14) V is a vector space. Mark each statement True or False. a. The number of...
14) V is a vector space. Mark each statement True or False. a. The number of pivot columns of a matrix equals the dimension of its column space. b. A plane in R' is a two-dimensional subspace of R'. c. The dimension of the vector space P, is 4. d. If dim V = n and S is a linearly independent set in V. then S is a basis for V. e. If a set fv.....v} spans a finite-dimensional vector...
DETAILS LARLINALG8 4.R.084. ASK YOUR TEACHER Determine whether each statement is true or false. If a...
DETAILS LARLINALG8 4.R.084. ASK YOUR TEACHER Determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. () The set w = {(0,x2,x): and X" are real numbers) is a subspace of R. False, this set is not closed under addition...
Question 1 1 pts If vv - list(a-1,b-2) why doesn't as.vector(vv) work to coerce vw to...
Question 1 1 pts If vv - list(a-1,b-2) why doesn't as.vector(vv) work to coerce vw to an atomic vector? Not applicable: The code returns an error. vv is already a vector atomic vectors cannot have named elements elements of an atomic vector must be of the same type. Question 2 2 pts Suppose ll<-list(a-1,b-c(2,3)). How do we replace the value 3 with the missing data code NA? 0 11[[2]][2] <-NA ﹁ ll <-as.na(II[[2]]) 0 ll[[22]] <-NA is.na([211) <-2 Question3 1...
Question 5 Let V be a subspace of R100, and let S be a set of vectors such that y = = 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 number of nonzero rows in a REF of A the number of vectors in S the rank of A O the number of "leading 1s"...
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...
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...
(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...
solve the linear algebra question
1. (6 points) Let S be a subspace of R3 spanned by the columns of the matrix [1 2 0 1 1] 2 4 1 1 0 3 6 1 2 1 Find a basis of S. What is the dimension of S?
3. (15 pts) Let A be an m x n matrix with rank r, and let V = C(A). (a) V CIRP for what p? (b) What is V. in terms of a fundamental subspace for A? (c) How many vectors are in a basis for V, and how many in a basis for v 1? (d) For what m, n, and r docs Ax=b have a solution for every b? (e) Is a set of r vectors in V...
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
14) V is a vector space. Mark each statement True or False. a. The number of pivot columns of a matrix equals the dimension of its column space. b. A plane in R' is a two-dimensional subspace of R'. c. The dimension of the vector space P, is 4. d. If dim V = n and S is a linearly independent set in V. then S is a basis for V. e. If a set fv.....v} spans a finite-dimensional vector...
DETAILS LARLINALG8 4.R.084. ASK YOUR TEACHER Determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. () The set w = {(0,x2,x): and X" are real numbers) is a subspace of R. False, this set is not closed under addition...
Question 1 1 pts If vv - list(a-1,b-2) why doesn't as.vector(vv) work to coerce vw to an atomic vector? Not applicable: The code returns an error. vv is already a vector atomic vectors cannot have named elements elements of an atomic vector must be of the same type. Question 2 2 pts Suppose ll<-list(a-1,b-c(2,3)). How do we replace the value 3 with the missing data code NA? 0 11[[2]][2] <-NA ﹁ ll <-as.na(II[[2]]) 0 ll[[22]] <-NA is.na([211) <-2 Question3 1...
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