![5. [20pts] Suppose A is a 3x3 matrix with independent eigenvector x,x2,x, satisfying Ay bx, -cx for any vector y ax +bx, +cx,](http://img.homeworklib.com/images/94cb4ee5-746e-4af7-822d-7c31e0187dbe.png?x-oss-process=image/resize,w_560)
I think the lambdas are (0, 1, -1)
then how can I solve (b), (c) ??
Thank YOU!
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I think the lambdas are (0, 1, -1) then how can I solve (b), (c) ?? Thank YOU! 5. [20pts] Suppose A is a 3x3 matrix wit...
7 -4 8 Consider the 3x3 matrix A= 4 -1 8 -4 4 - 5 (a)...
7 -4 8 Consider the 3x3 matrix A= 4 -1 8 -4 4 - 5 (a) Find the eigenvalues of A. Show every step of your work. The key to successful factorization is not to distribute anything in the determinant until you have factored out everything you possibly can from all terms. When your factorization is complete, it should show the algebraic multiplicity of each eigenvalue. (b) What is/are the eigenvector(s) corresponding to each eigenvalue? (c) What are the eigenspaces?
Suppose A is a symmetric 3 by 3 matrix with eigenvalues 0, 1, 2 (a) What...
Suppose A is a symmetric 3 by 3 matrix with eigenvalues 0, 1, 2 (a) What properties 4. can be guaranteed for the corresponding unit eigenvectors u, v, w? In terms of u, v, w describe the nullspace, left nullspace, (b) row space, and column space of A (c) Find a vector x that satisfies Ax v +w. Is x unique? Under what conditions on b does Ax = b have a solution? (d) (e) If u, v, w are...
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...
Could you please just solve Question (i) A: Thanks 3. For each of the following matrices,...
Could you please just solve Question
(i) A: Thanks
3. For each of the following matrices, a. Determine the characteristic polynomial corresponding to the matrix. b. Find the eigenvalues of the matrix. c. For each eigenvalue, determine the corresponding eigenspace as a span of vectors. d. Determine an eigenvector corresponding to each eigenvalue. e. Pick one eigenvalue of each matrix and the corresponding eigenvector chosen in part (d) and verify that they are indeed an eigenvalue and eigenvector of the...
A1. Let (A, B, C, D) be a SISO system in which A is a (n x n) complex matrix and B a (n x 1) column vector, let -1 V =...
A1. Let (A, B, C, D) be a SISO system in which A is a (n x n) complex matrix and B a (n x 1) column vector, let -1 V = {£ajA*B: aj e C; j= 0, ...,n- (i) Show that V is a complex vector space. (ii) Show that V has dimension one, if and only if B is an eigenvector of A AX for X E V. Show that S defines a linear map from S: V...
I know A-D. Please do E-G only. Thanks! [ 1 ] [ 0 ] = W,...
I know A-D. Please do E-G only. Thanks!
[ 1 ]
[ 0 ] = W, W_2 is found in part F
[ 1 ]
3. (Taken from Boyce & DiPrima) Consider the 3-dimensional system of linear equations Ti 11] X' = AX = 2 1 -1 x 1-3 2 4 (a) Show that the three eigenvalues of the coefficient matrix, A, are 1, = lyd = 2. This is an eigenvalue of multiplicity 3. (b) Show that all the...
I need all details. Thx 2. Give an example of a matrix with the indicated properties. If the property cannot be attained, explain why not (a) A is 2 x 4 and has rank 3. (b) A is 3 × 3 and has dete...
I need all details. Thx
2. Give an example of a matrix with the indicated properties. If the property cannot be attained, explain why not (a) A is 2 x 4 and has rank 3. (b) A is 3 × 3 and has determinant 1. (c) A is 3 × 6 and has a 3 dimensional row space and a 6 dinensional column space (d) A is 3 × 3 and has a 2 dimensional null space. (e) A is...
SOLVE ANY (2.b) Pts 15 Suppose A' is any matrix whe row reduced echelon form A Show there is a matris D' Mn a wuch thnt A iDMa such that A I Question 3: The matrix condition B2B Ps 30: In this...
SOLVE ANY
(2.b) Pts 15 Suppose A' is any matrix whe row reduced echelon form A Show there is a matris D' Mn a wuch thnt A iDMa such that A I Question 3: The matrix condition B2B Ps 30: In this problen B is n (3.a) Pts 10: If a is an eigenvector for B, what is the attached eigenvalue (3. b) Pts 10: Irge R", why is BU) perpendieular to Bur square, n x n, smmetric matris satisfying...
I got part a to be 1 and .92 1. Given the following matrix A- 05 .97 a. calculate the eigenvalues by using RStudio. b. calculate the integer values of the eigenvectors, vi and v2 by hand only calc...
I got part a to be 1 and .92
1. Given the following matrix A- 05 .97 a. calculate the eigenvalues by using RStudio. b. calculate the integer values of the eigenvectors, vi and v2 by hand only calculate the weights ci and c2, such that: c. given x d. Calculating the long-term behavior of a dynamic system: Remembering, in general Ax Ax fill in using ci and c2, the eigenvalues λ1 and λ2 and vectors vi and v2. e....
1. Formulate the following problem as least squares problems. For each problem, give a matrix A and a vector b such that the problem can be expressed as argmin |lAx - bllz (you are not asked to solve...
1. Formulate the following problem as least squares problems. For each problem, give a matrix A and a vector b such that the problem can be expressed as argmin |lAx - bllz (you are not asked to solve the problems. Just state define matrix A and vector b) Ỉ + 2x + 3x + (x1-x2 + x3-1)'t (-ri-4x2 + 2)2; à. minimize x b. minimize xTx + I|Bx - dll2, where the pxn matrix B and the p-vector d are...
7 -4 8 Consider the 3x3 matrix A= 4 -1 8 -4 4 - 5 (a) Find the eigenvalues of A. Show every step of your work. The key to successful factorization is not to distribute anything in the determinant until you have factored out everything you possibly can from all terms. When your factorization is complete, it should show the algebraic multiplicity of each eigenvalue. (b) What is/are the eigenvector(s) corresponding to each eigenvalue? (c) What are the eigenspaces?
Suppose A is a symmetric 3 by 3 matrix with eigenvalues 0, 1, 2 (a) What properties 4. can be guaranteed for the corresponding unit eigenvectors u, v, w? In terms of u, v, w describe the nullspace, left nullspace, (b) row space, and column space of A (c) Find a vector x that satisfies Ax v +w. Is x unique? Under what conditions on b does Ax = b have a solution? (d) (e) If u, v, w are...
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...
Could you please just solve Question
(i) A: Thanks
3. For each of the following matrices, a. Determine the characteristic polynomial corresponding to the matrix. b. Find the eigenvalues of the matrix. c. For each eigenvalue, determine the corresponding eigenspace as a span of vectors. d. Determine an eigenvector corresponding to each eigenvalue. e. Pick one eigenvalue of each matrix and the corresponding eigenvector chosen in part (d) and verify that they are indeed an eigenvalue and eigenvector of the...
A1. Let (A, B, C, D) be a SISO system in which A is a (n x n) complex matrix and B a (n x 1) column vector, let -1 V = {£ajA*B: aj e C; j= 0, ...,n- (i) Show that V is a complex vector space. (ii) Show that V has dimension one, if and only if B is an eigenvector of A AX for X E V. Show that S defines a linear map from S: V...
I know A-D. Please do E-G only. Thanks!
[ 1 ]
[ 0 ] = W, W_2 is found in part F
[ 1 ]
3. (Taken from Boyce & DiPrima) Consider the 3-dimensional system of linear equations Ti 11] X' = AX = 2 1 -1 x 1-3 2 4 (a) Show that the three eigenvalues of the coefficient matrix, A, are 1, = lyd = 2. This is an eigenvalue of multiplicity 3. (b) Show that all the...
I need all details. Thx
2. Give an example of a matrix with the indicated properties. If the property cannot be attained, explain why not (a) A is 2 x 4 and has rank 3. (b) A is 3 × 3 and has determinant 1. (c) A is 3 × 6 and has a 3 dimensional row space and a 6 dinensional column space (d) A is 3 × 3 and has a 2 dimensional null space. (e) A is...
SOLVE ANY
(2.b) Pts 15 Suppose A' is any matrix whe row reduced echelon form A Show there is a matris D' Mn a wuch thnt A iDMa such that A I Question 3: The matrix condition B2B Ps 30: In this problen B is n (3.a) Pts 10: If a is an eigenvector for B, what is the attached eigenvalue (3. b) Pts 10: Irge R", why is BU) perpendieular to Bur square, n x n, smmetric matris satisfying...
I got part a to be 1 and .92
1. Given the following matrix A- 05 .97 a. calculate the eigenvalues by using RStudio. b. calculate the integer values of the eigenvectors, vi and v2 by hand only calculate the weights ci and c2, such that: c. given x d. Calculating the long-term behavior of a dynamic system: Remembering, in general Ax Ax fill in using ci and c2, the eigenvalues λ1 and λ2 and vectors vi and v2. e....
1. Formulate the following problem as least squares problems. For each problem, give a matrix A and a vector b such that the problem can be expressed as argmin |lAx - bllz (you are not asked to solve the problems. Just state define matrix A and vector b) Ỉ + 2x + 3x + (x1-x2 + x3-1)'t (-ri-4x2 + 2)2; à. minimize x b. minimize xTx + I|Bx - dll2, where the pxn matrix B and the p-vector d are...
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