Homework Answers
Please find the attached files for the answer. If you still have some doubts in this answer, comment below. "Col." means column in the answer. In the first page, there is a useful note to multiply two matrices. I find the inverse of R using that note.
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13. Let W = {ī E R4 : Ai = 0} for some constant matrix A....
13. Let W = {ī E R4 : Ai = 0} for some constant matrix A. Suppose all solutions are 1 ES1 lo 1 +r , where t,s,r can be any real numbers. Let S = 0 1 'lo (a) (3 pts) What must the dimensions of the matrix A be? Justify briefly. (b) (8 pts) Show directly from the definition that S is a linearly independent set. (c) (6 pts) Without doing any further) computations, explain why S is...
2. Given the columns of the matrix u v w 0 1 2 0-1 0 0 r S t -1 021 01 0 For each of the sets of ...
Please solve using matrices and not equations.
Thanks.
2. Given the columns of the matrix u v w 0 1 2 0-1 0 0 r S t -1 021 01 0 For each of the sets of vectors given below, answer the following questions: (i) Is the set linearly independent? 1 Does the set span (iii Does the vector a- (a) S (r, s, t, u) (b) T fr,t, 0, u) (c) U = {r, t, w, u, v} (3,2,1,5)...
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...
3. Let A 2 -30 1 0 -2 2 0 (i) Compute the determinant of A...
3. Let A 2 -30 1 0 -2 2 0 (i) Compute the determinant of A using the cofactor expansion technique along (a) row 1 and (b) column 3. (ii) In trying to find the inverse of A, applying four elementary row operations reduces the aug- mented matrix [A1] to -2 0 0 0 0 -2 2 1 3 0 1 0 1 0 -2 Continue with row reductions to obtain the augmented matrix [1|A-') and thus give the in-...
Let M be an n x n matrix with each entry equal to either 0 or 1. Let mij denote the entry in row i and column j. A diago...
Let M be an n x n matrix with each entry equal to either 0 or 1. Let mij denote the entry in row i and column j. A diagonal entry is one of the form mii for some i. Swapping rows i and j of the matrix M denotes the following action: we swap the values mik and mjk for k = 1,2, ... , n. Swapping two columns is defined analogously. We say that M is rearrangeable if...
3 -5 0 1 0 2 0 0 Consider the matrix A= -1 -1 0 3...
3 -5 0 1 0 2 0 0 Consider the matrix A= -1 -1 0 3 1 0 -3 2 Which of the following statements about the determinant of A is true? det(2A) = 2 det A det(-A) = det A O Multiplying any row of Aby -1 does not change det A Interchanging two rows of A does not change det A
) Let A be the following matrix: 13 0 2 0 2 2 0 0 6...
) Let A be the following matrix: 13 0 2 0 2 2 0 0 6 (a) Enter its characteristic equation below. Note you must use p as the parameter instead of , and you must enter your answer as a equation, with the equals sign. (b) Enter the eigenvalues of the matrix, including any repetition. For example 16,16,24. 5 (c) Find the eigenvectors, and then use Gram-Schmidt to find an orthonormal basis for each eigenvalue's eigenspace. Build an orthogonal...
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...
What is the R code and result in Rstudio 1. The following data gives, for each...
What is the R code and result in Rstudio
1. The following data gives, for each amount by which an elastic band is stretched over the end of a ruler, the distance that the band moved when released: stretch 46 54 48 50 44 4 52 distance 148 182 173166 109 141 166 Create a data frame in R with two columns that contain "stretch and "dis tance" respectively. Plot the distance versus the stretch using plot) function What trend...
In the vector space R, let 8 {(1,3,0), (1, -3, 0), (0, 2, 2)}. (a) (6...
In the vector space R, let 8 {(1,3,0), (1, -3, 0), (0, 2, 2)}. (a) (6 points) Show that y is a basis of R3. (b) (7 points) Find the matrix [I,where I is the identity transform R3 R3 (c) (7 points) Using the matrix [I, convert the vector (r, y, z) into coordinates with respect to y instead of B. In other words, find ((x, y, z)] {(1,0,0), (0, 1,0), (0,0, 1)} be the standard basis, and let
13. Let W = {ī E R4 : Ai = 0} for some constant matrix A. Suppose all solutions are 1 ES1 lo 1 +r , where t,s,r can be any real numbers. Let S = 0 1 'lo (a) (3 pts) What must the dimensions of the matrix A be? Justify briefly. (b) (8 pts) Show directly from the definition that S is a linearly independent set. (c) (6 pts) Without doing any further) computations, explain why S is...
Please solve using matrices and not equations.
Thanks.
2. Given the columns of the matrix u v w 0 1 2 0-1 0 0 r S t -1 021 01 0 For each of the sets of vectors given below, answer the following questions: (i) Is the set linearly independent? 1 Does the set span (iii Does the vector a- (a) S (r, s, t, u) (b) T fr,t, 0, u) (c) U = {r, t, w, u, v} (3,2,1,5)...
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...
3. Let A 2 -30 1 0 -2 2 0 (i) Compute the determinant of A using the cofactor expansion technique along (a) row 1 and (b) column 3. (ii) In trying to find the inverse of A, applying four elementary row operations reduces the aug- mented matrix [A1] to -2 0 0 0 0 -2 2 1 3 0 1 0 1 0 -2 Continue with row reductions to obtain the augmented matrix [1|A-') and thus give the in-...
3 -5 0 1 0 2 0 0 Consider the matrix A= -1 -1 0 3 1 0 -3 2 Which of the following statements about the determinant of A is true? det(2A) = 2 det A det(-A) = det A O Multiplying any row of Aby -1 does not change det A Interchanging two rows of A does not change det A
) Let A be the following matrix: 13 0 2 0 2 2 0 0 6 (a) Enter its characteristic equation below. Note you must use p as the parameter instead of , and you must enter your answer as a equation, with the equals sign. (b) Enter the eigenvalues of the matrix, including any repetition. For example 16,16,24. 5 (c) Find the eigenvectors, and then use Gram-Schmidt to find an orthonormal basis for each eigenvalue's eigenspace. Build an orthogonal...
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...
What is the R code and result in Rstudio
1. The following data gives, for each amount by which an elastic band is stretched over the end of a ruler, the distance that the band moved when released: stretch 46 54 48 50 44 4 52 distance 148 182 173166 109 141 166 Create a data frame in R with two columns that contain "stretch and "dis tance" respectively. Plot the distance versus the stretch using plot) function What trend...
In the vector space R, let 8 {(1,3,0), (1, -3, 0), (0, 2, 2)}. (a) (6 points) Show that y is a basis of R3. (b) (7 points) Find the matrix [I,where I is the identity transform R3 R3 (c) (7 points) Using the matrix [I, convert the vector (r, y, z) into coordinates with respect to y instead of B. In other words, find ((x, y, z)] {(1,0,0), (0, 1,0), (0,0, 1)} be the standard basis, and let
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