HomeworkLib
Question

✓ 3.32 This matrix has distinct eigenvalues. 1 2 1 6 -1 0 -1 -2 -1) (a) Diagonalize it. (b) Find a basis with respect to whic

math   Advanced-Math   
0 0
Add a comment Improve this question Transcribed image text
Next > < Previous
Sort answers by oldest

Homework Answers

Answer #1

C(A) = 1 A-dil= = = 1-1 -2 -1-2/ - - x + 12 ** -x ( +-12) --> (2+4) (6-3) di=o, da = - 4 Az = 3 A-DI -1 -2 -U AV= av (A-20 v=Det = 1024 1 5 2 1 A-d I = 1 6 3 or - 1-1 -23 oot. R, ZR opt, Ro Ro -6R, 8 R₂ R3 +R, R3 - (-) Re opt R3 T13 opt R, - R - (²)- . . A- 13 I = 16 -40 -1 -2 -4 opt. R. IR ~ 16 -1 - -4 ol - -4) opt Ra Rg - 6R, opt Rz Rz + R, -1 1/2 11 o Ra 1 – 3-2 R2 -1ni trg=0 n = -13 na = 3 4 The sol set = Let us = 1 1 -33 no The Diagonal matrix o-diag & [ 21, 22, Ag] lo o 3 The eigenvector

0 0
Add a comment
Know the answer?
Add Answer to:
✓ 3.32 This matrix has distinct eigenvalues. 1 2 1 6 -1 0 -1 -2 -1)...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions

  • The symmetric matrix A below has distinct eigenvalues 10,-2 and-8. Find an orthogonal matrix P and...

    The symmetric matrix A below has distinct eigenvalues 10,-2 and-8. Find an orthogonal matrix P and a diagonal matrix D such that pTAP-Duse the square root symbol 'where needed to give an exact value for your answer. -1 47 A- 4 2-4 0 0 0] P=10 0 0| D=10 0 0

  • Find the eigenvalues of the given matrix. [-14 -6 36 16 1) A) -2.-4 B)-4 C)-2...

    Find the eigenvalues of the given matrix. [-14 -6 36 16 1) A) -2.-4 B)-4 C)-2 D) -24 The characteristic polynomial of a 5 5 matrix is given below. Find the eigenvalues and their multiplicities 2) A5 - 24A4-189A3-486A2 2) A) 0 (multiplicity 2),-9 (multiplicity 2),-6 (multiplicity 1) B) 0 (multiplicity 1),9 (multiplicity 3), 6 (multiplicity ) C) 0 (multiplicity 2),9 (multiplicity 2),6 (multiplicity 1) D) 0 (multiplicity 2),-9 (multiplicity 2),6 (multiplicity 1) Diagonalize A- PDP-1 the matrix A, if...

  • Let 4-β 0 0 A=1 0 4-3 024-β where β > 0 is a parameter. (a) Find the eigenvalues of A (note the eigenvalues will be functions of β). (b) Determine the values of β for which the matrix A is positiv...

    Let 4-β 0 0 A=1 0 4-3 024-β where β > 0 is a parameter. (a) Find the eigenvalues of A (note the eigenvalues will be functions of β). (b) Determine the values of β for which the matrix A is positive definite. Determine the values of β for which the matrix A is positive semidefinite. (c) For each eigenvalue of A, find a basis for the corresponding eigenspace. (d) Find an orthonormal basis for R3 consisting of eigenvectors of...

  • Let matrix M = -8 -24 -12 0 4 0 6 12 10 (a) Find the...

    Let matrix M = -8 -24 -12 0 4 0 6 12 10 (a) Find the eigenvalues of M (b) For each eigenvalue λ of M, find a basis for the eigenspace of λ. (c) Is the matrix M diagonalizable? If so, find matrices D and P such that D is a diagonal matrix and M=PDP^−1. If not, explain carefully why not.

  • Let matrix M = -8 -24 12 0 4 0 6 12 10 (a) Find the...

    Let matrix M = -8 -24 12 0 4 0 6 12 10 (a) Find the eigenvalues of M (b) For each eigenvalue λ of M, find a basis for the eigenspace of λ. (c) Is the matrix M diagonalizable? If so, find matrices D and P such that D is a diagonal matrix and M=PDP−1. If not, explain carefully why not.

  • For the 3×2 matrix A: a) Determine the eigenvalues of ATA, and confirm that your eigenvalues...

    For the 3×2 matrix A: a) Determine the eigenvalues of ATA, and confirm that your eigenvalues are consistent with the trace and determinant of ATA. b) Find an eigenvector for each eigenvalue of ATA. c) Find an invertible matrix P and a diagonal matrix D such that P-1(ATA)P = D. d) Find the singular value decomposition of the matrix A; that is, find matrices U, Σ, and V such that A = UΣVT. e) What is the best rank 1...

  • (1 point) The matrix 2 -1 0 A2-3 -1 has three distinct real eigenvalues if and only if

    (1 point) The matrix 2 -1 0 A2-3 -1 has three distinct real eigenvalues if and only if (1 point) The matrix 2 -1 0 A2-3 -1 has three distinct real eigenvalues if and only if

  • [-5 0 5 5 0 -5 0 0 0 0 -5 0 0 0-5 0 (1 point) 2 The matrix A- has two distinct eigenvalues λ1 < λ...

    [-5 0 5 5 0 -5 0 0 0 0 -5 0 0 0-5 0 (1 point) 2 The matrix A- has two distinct eigenvalues λ1 < λ2. Find the eigenvalues and a basis for each eigenspace. whose eigenspace has a basis of , whose eigenspace has a basis of | [1,0,0,1] Note: You can earn partial credit on this problem Preview My Answers Submit Answers Your score was recorded. You have attempted this problem 9 times. You received a...

  • 0 2 0 A = 20 Lo 0 1 then the eigenvalues of A are 1...

    0 2 0 A = 20 Lo 0 1 then the eigenvalues of A are 1 = 1,2= 2 and X = -2 (all with multiplicity of 1) (A) Find an ordignormal basis for the eigenspace corresponding to X=1 (B) Find an onHonormal basis for the eigenspace corresponding to 1 = 2. (C) Find an arxhonormal basis for the eigenspace corresponding to 1 = -2. (D) Provide an orthogonal matrix P and a diagonal matrix D such that PAP=D.

  • 8. Let A be an nxn matrix with distinct n eigenvalues X1, 2... (a) What is...

    8. Let A be an nxn matrix with distinct n eigenvalues X1, 2... (a) What is the determinant of A. (b) If a 2 x 2 matrix satisfies tr(AP) = 5, tr(A) = 3, then find det(A). (The trace of a square matrix A, denoted by tr(A), is the sum of the elements on the main diagonal of A.

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT