Homework Answers
17. Suppose that 0 00 0 1 1 0 0 0 0 0 2 0 0...
17. Suppose that 0 00 0 1 1 0 0 0 0 0 2 0 0 0 0 0 0 100 A= 0 0 0 0 0 1 0 0 1 0 0 Find: 1) QH decomposition of A 2) the pseudo-inverse of A 3) an orthonormal basis for each of the four fundamental subspaces of A 4) the projection matrix of the column space and the projection matrix of the row space of A
17. Suppose that 0 00...
How can I get the (a) 3*2 matrix A? x 7. [30pts] Let V be the subspace of R consisting of vectors satisfying x- y+z = 0...
How can I get the (a) 3*2 matrix A?
x 7. [30pts] Let V be the subspace of R consisting of vectors satisfying x- y+z = 0 y (a) Find a 3x2 matrix A whose column space is V and the entries a a1 0 = (b) Find an orthonormal basis for V by applying the Gram-Schmidt procedure (c) Find the projection matrix P projecting onto the left nullspace (not the column space) of A (d) Find an SVD (A...
1 4 2 1 7.[12pts) Let A = 0 1 1-2 -8 -4 -2 (a) Find...
1 4 2 1 7.[12pts) Let A = 0 1 1-2 -8 -4 -2 (a) Find bases for the four fundamental subspaces of the matrix A. Basis for n(A) = nullspace of A: Basis for N(4")= nullspace of A": Basis for col(A) = column space of A: Basis for col(A) = column space of A': () Give a vector space that is isomorphic to col (A) N(A).
2) (8 points) Consider the matrix A=10 1-1-2 » Find the full set of solutions to Ai-1 0 What is t...
2) (8 points) Consider the matrix A=10 1-1-2 » Find the full set of solutions to Ai-1 0 What is the rank of A, give a basis of its column space and its row space. What is the dimension of its Nullspace and its left Nullspace? (you do not need to compute these subspaces) .Find a basis of its left nullspace (hint: you may need to compute RREF(AT).
2) (8 points) Consider the matrix A=10 1-1-2 » Find the full...
I need help with parts c and d of this question. Some concept clarification would be great. 3. Consider the following matrix A= 3 6 (a) Compute AAT and its eigenvalues and unit eigenvectors. (b) Find...
I need help with parts c and d of this question. Some concept
clarification would be great.
3. Consider the following matrix A= 3 6 (a) Compute AAT and its eigenvalues and unit eigenvectors. (b) Find the SVD by computing the matrices U, V, Σ (c) From the u's and v's in (b), write down orthonormal bases for all four fundamental subspaces (i.e., row space, column space, null space, left null space) of the matrix A. (d) Compute the pseudoinverse...
Find a basis for the row space of A. 1 -1 3 2 -3 8 A-0...
Find a basis for the row space of A. 1 -1 3 2 -3 8 A-0 1 -2 Find a basis for the null space of A. Verify that every vector in row(A) is orthogonal to every vector in null(A). Need Help? Submit Answer Save Progress Practice Another Version 17. -12 points PooleLinAlg4 5.2.009. Find a basis for the column space of A. My Notes Ask Your Tea 1-1 3 5 2 1 A- 012 T. Find a basis for...
Problem 2 A matrix A is given by 2 3 0 1 7 2 1 13...
Problem 2 A matrix A is given by 2 3 0 1 7 2 1 13 16 3 -5 -3 8 22 -1 -1 -11 -18 Find a basis for N(A) (the null space of A). Find a basis for RaneA) = C(A) (the range, or column space of A)
Problem 2 A matrix A is given by 2 3 0 1 7 2 1 13 16 3 -5 -3 8 22 -1 -1 -11 -18 Find a basis for...
Consider the matrix 0 4 8 24 0-3-6 3 18 A-0 24 2 -12 0 -2-3...
Consider the matrix 0 4 8 24 0-3-6 3 18 A-0 24 2 -12 0 -2-3 0 7 0 3 5 [51 [51 a) Find a basis for the row space Row(A) of A (b) Find a basis for the column space Col(A) of A (c) Find a basis space d) Find the rank Rank(A) and the nullity of A (e) Determine if the vector v (1,4,-2,5,2) belongs to the null space of A. - As always,[5 is for the...
1. 2. 3. 4. 5. Given that B = {[1 7 3], [ – 2 –7...
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Given that B = {[1 7 3], [ – 2 –7 – 3), [6 23 10]} is a basis of R' and C = {[1 0 0], [-4 1 -2], [-2 1 - 1]} is another basis for R! find the transition matrix that converts coordinates with respect to base B to coordinates with respect to base C. Preview Find a single matrix for the transformation that is equivalent to doing the following four transformations...
2. (12 pts) Given the matrix in a R R-E form: [1 1 0 0 3...
2. (12 pts) Given the matrix in a R R-E form: [1 1 0 0 3 0 0 0 1 0 -2 0 A = 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 (a) (6 pts) Find rank(A) and nullity(A), and nullity(AT). (b) (2 pts) Find a basis for the row space of A. (c) (2 pts) Find a basis for the column space of A. (d) (2 pts) Find a...
17. Suppose that 0 00 0 1 1 0 0 0 0 0 2 0 0 0 0 0 0 100 A= 0 0 0 0 0 1 0 0 1 0 0 Find: 1) QH decomposition of A 2) the pseudo-inverse of A 3) an orthonormal basis for each of the four fundamental subspaces of A 4) the projection matrix of the column space and the projection matrix of the row space of A
17. Suppose that 0 00...
How can I get the (a) 3*2 matrix A?
x 7. [30pts] Let V be the subspace of R consisting of vectors satisfying x- y+z = 0 y (a) Find a 3x2 matrix A whose column space is V and the entries a a1 0 = (b) Find an orthonormal basis for V by applying the Gram-Schmidt procedure (c) Find the projection matrix P projecting onto the left nullspace (not the column space) of A (d) Find an SVD (A...
1 4 2 1 7.[12pts) Let A = 0 1 1-2 -8 -4 -2 (a) Find bases for the four fundamental subspaces of the matrix A. Basis for n(A) = nullspace of A: Basis for N(4")= nullspace of A": Basis for col(A) = column space of A: Basis for col(A) = column space of A': () Give a vector space that is isomorphic to col (A) N(A).
2) (8 points) Consider the matrix A=10 1-1-2 » Find the full set of solutions to Ai-1 0 What is the rank of A, give a basis of its column space and its row space. What is the dimension of its Nullspace and its left Nullspace? (you do not need to compute these subspaces) .Find a basis of its left nullspace (hint: you may need to compute RREF(AT).
2) (8 points) Consider the matrix A=10 1-1-2 » Find the full...
I need help with parts c and d of this question. Some concept
clarification would be great.
3. Consider the following matrix A= 3 6 (a) Compute AAT and its eigenvalues and unit eigenvectors. (b) Find the SVD by computing the matrices U, V, Σ (c) From the u's and v's in (b), write down orthonormal bases for all four fundamental subspaces (i.e., row space, column space, null space, left null space) of the matrix A. (d) Compute the pseudoinverse...
Find a basis for the row space of A. 1 -1 3 2 -3 8 A-0 1 -2 Find a basis for the null space of A. Verify that every vector in row(A) is orthogonal to every vector in null(A). Need Help? Submit Answer Save Progress Practice Another Version 17. -12 points PooleLinAlg4 5.2.009. Find a basis for the column space of A. My Notes Ask Your Tea 1-1 3 5 2 1 A- 012 T. Find a basis for...
Problem 2 A matrix A is given by 2 3 0 1 7 2 1 13 16 3 -5 -3 8 22 -1 -1 -11 -18 Find a basis for N(A) (the null space of A). Find a basis for RaneA) = C(A) (the range, or column space of A)
Problem 2 A matrix A is given by 2 3 0 1 7 2 1 13 16 3 -5 -3 8 22 -1 -1 -11 -18 Find a basis for...
Consider the matrix 0 4 8 24 0-3-6 3 18 A-0 24 2 -12 0 -2-3 0 7 0 3 5 [51 [51 a) Find a basis for the row space Row(A) of A (b) Find a basis for the column space Col(A) of A (c) Find a basis space d) Find the rank Rank(A) and the nullity of A (e) Determine if the vector v (1,4,-2,5,2) belongs to the null space of A. - As always,[5 is for the...
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Given that B = {[1 7 3], [ – 2 –7 – 3), [6 23 10]} is a basis of R' and C = {[1 0 0], [-4 1 -2], [-2 1 - 1]} is another basis for R! find the transition matrix that converts coordinates with respect to base B to coordinates with respect to base C. Preview Find a single matrix for the transformation that is equivalent to doing the following four transformations...
2. (12 pts) Given the matrix in a R R-E form: [1 1 0 0 3 0 0 0 1 0 -2 0 A = 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 (a) (6 pts) Find rank(A) and nullity(A), and nullity(AT). (b) (2 pts) Find a basis for the row space of A. (c) (2 pts) Find a basis for the column space of A. (d) (2 pts) Find a...
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